{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Random Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Independent Processes\n",
    "\n",
    "The independence of random signals is a desired property in many applications of statistical signal processing, as well as uncorrelatedness and orthogonality. The concept of independence is introduced in the following together with a discussion of the links to uncorrelatedness and orthogonality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition\n",
    "\n",
    "Two stochastic events are said to be [independent](https://en.wikipedia.org/wiki/Independence_(probability_theory)) if the probability of occurrence of one event is not affected by the occurrence of the other event. Or more specifically, if their joint probability equals the product of their individual probabilities. In terms of the bivariate probability density function (PDF) of two continuous-amplitude real-valued random processes $x[k]$ and $y[k]$ this reads\n",
    "\n",
    "\\begin{equation}\n",
    "p_{xy}(\\theta_x, \\theta_y, k_x, k_y) = p_x(\\theta_x, k_x) \\cdot p_y(\\theta_y, k_y)\n",
    "\\end{equation}\n",
    "\n",
    "where $p_x(\\theta_x, k_x)$ and $p_y(\\theta_y, k_y)$ denote the univariate ([marginal](https://en.wikipedia.org/wiki/Marginal_distribution)) PDFs of the random processes for the time-instances $k_x$ and $k_y$, respectively. The bivariate PDF of two independent random processes is given by the multiplication of their univariate PDFs. It follows that the [second-order ensemble average](ensemble_averages.ipynb#Second-Order-Ensemble-Averages) for a linear mapping is given as\n",
    "\n",
    "\\begin{equation}\n",
    "E\\{ x[k_x] \\cdot y[k_y] \\} = E\\{ x[k_x] \\} \\cdot E\\{ y[k_y] \\}\n",
    "\\end{equation}\n",
    "\n",
    "The linear second-order ensemble average of two independent random signals is equal to the multiplication of their linear first-order ensemble averages. For jointly wide-sense stationary (WSS) processes, the bivariate PDF does only depend on the difference $\\kappa = k_x - k_y$ of the time instants. Hence, two jointly WSS random signals are independent if \n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "p_{xy}(\\theta_x, \\theta_y, \\kappa) &= p_x(\\theta_x, k_x) \\cdot p_y(\\theta_y, k_x - \\kappa) \\\\\n",
    "&= p_x(\\theta_x) \\cdot p_y(\\theta_y, \\kappa)\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "Above bivariate PDF is rewritten using the definition of [conditional probabilities](https://en.wikipedia.org/wiki/Conditional_probability) in order to specialize the definition of independence to one WSS random signal $x[k]$ \n",
    "\n",
    "\\begin{equation}\n",
    "p_{xy}(\\theta_x, \\theta_y, \\kappa) = p_{y|x}(\\theta_x, \\theta_y, \\kappa) \\cdot p_x(\\theta_x)\n",
    "\\end{equation}\n",
    "\n",
    "where $p_{y|x}(\\theta_x, \\theta_y, \\kappa)$ denotes the conditional probability that $y[k - \\kappa]$ takes the amplitude value $\\theta_y$ under the condition that $x[k]$ takes the amplitude value $\\theta_x$. Under the assumption that $y[k-\\kappa] = x[k-\\kappa]$ and substituting $\\theta_x$ and $\\theta_y$ by $\\theta_1$ and $\\theta_2$, independence for one random signal is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "p_{xx}(\\theta_1, \\theta_2, \\kappa) = \n",
    "\\begin{cases}\n",
    "p_x(\\theta_1) \\cdot \\delta(\\theta_2 - \\theta_1) & \\text{for } \\kappa = 0  \\\\\n",
    "p_x(\\theta_1) \\cdot p_x(\\theta_2, \\kappa) & \\text{for } \\kappa \\neq 0\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "since the conditional probability $p_{x[k]|x[k-\\kappa]}(\\theta_1, \\theta_2, \\kappa) = \\delta(\\theta_2 - \\theta_1)$ for $\\kappa = 0$ since this represents a sure event. The bivariate PDF of an independent random signal is equal to the product of the univariate PDFs of the signal and the time-shifted signal for $\\kappa \\neq 0$. A random signal for which this condition does not hold shows statistical dependencies between samples. These dependencies can be exploited for instance for coding or prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Comparison of bivariate PDF and product of marginal PDFs\n",
    "\n",
    "The following example estimates the bivariate PDF $p_{xx}(\\theta_1, \\theta_2, \\kappa)$ of a WSS random signal $x[k]$ by computing its two-dimensional histogram. The univariate PDFs $p_x(\\theta_1)$ and $p_x(\\theta_2, \\kappa)$ are additionally estimated. Both the estimated bivariate PDF and the product of the two univariate PDFs $p_x(\\theta_1) \\cdot p_x(\\theta_2, \\kappa)$ are plotted for different $\\kappa$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA90AAAHaCAYAAAAdVCoXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAACKNElEQVR4nO3deXxU1f3/8ffMZAMhUQkkIGFRK6CI0qDsRdSiWFFxKS5FXFvEVgH1W3FjaQW3WrQKikWQWoVfRVqtqFAV1IIKAVpb94pCEYqgEECyzZzfH2mmxMw5Se7MZJKb1/PxmMcjueeee89dZs6cOeeeT8AYYwQAAAAAABIumOoCAAAAAADgVzS6AQAAAABIEhrdAAAAAAAkCY1uAAAAAACShEY3AAAAAABJQqMbAAAAAIAkodENAAAAAECS0OgGAAAAACBJaHQDAAAAAJAkNLoBAAAAAEgSGt0AAEh6++23NXLkSHXq1EmZmZnKy8tT//79dcMNN0TXmTJligKBgHbs2FHr9ubPn69AIKDPPvssumzRokU65phj1KJFCwUCAW3YsEGrVq3SlClTtGvXriQcVcPYu3evxo8frw4dOigrK0vHH3+8Fi5cmOpiAQDQKNDoBgA0ey+88IIGDBig4uJi3XPPPVq2bJkeeOABDRw4UIsWLfK0zR/84AdavXq12rdvL0n68ssvNXr0aB1xxBF66aWXtHr1ah111FFatWqVpk6d2qQb3eeee66eeOIJTZ48WS+++KJOOOEEXXTRRXrqqadSXTQAAFIuLdUFAAAg1e655x517dpVL7/8stLS/lc1Xnjhhbrnnns8bbNt27Zq27Zt9P+PPvpI5eXl+tGPfqQhQ4bEXebGYunSpVq+fLmeeuopXXTRRZKkoUOH6vPPP9dNN92kUaNGKRQKpbiUAACkDj3dAIBmb+fOncrNza3W4K4SDNasKv/zn//ooosuUk5OjvLy8nTFFVdo9+7d1dY5cHj5ZZddpkGDBkmSRo0apUAgoJNOOklTpkzRTTfdJEnq2rWrAoGAAoGAVqxY4SzvD3/4Q3Xq1Cn6/759+zRq1Ch17NhR77zzTn0PPy5LlixRq1atdMEFF1Rbfvnll+uLL77Q22+/3aDlAQCgsaGnGwDQ7PXv31+//e1vdd111+mSSy7Rd7/7XaWnp1vXP++88zRq1ChdeeWVevfddzVp0iRJ0uOPPx5z/dtvv10nnniirr32Wk2fPl1Dhw5Vdna2srOz9dVXX+k3v/mNnn322ehQ9KOPPtpZ3nXr1um73/2uJOnTTz/VyJEjlZ2draKiIuXl5dVY3xijcDhcp3MR64cHl3/84x/q0aNHjXy9evWKpg8YMKBe2wQAwE/o6QYANHt33XWXBg0apN/85jfq16+fDjroIA0cOFB33XWX9u7dW2P9K6+8UlOnTtWpp56qCRMm6Morr9TTTz8tY0zM7R9xxBHRhvR3vvMd9evXT0cffbQ6duwY7bHu3bu3+vXrp379+ik7O9ta1t27d+vTTz9VYWGhli1bphNOOEGDBg3Sq6++GrPBLUkrV65Uenp6nV4HTvxWFzt37tShhx5aY3nVsp07d9ZrewAA+A093QCAZq9NmzZ64403tHbtWr3yyitau3atVqxYoUmTJunRRx/VmjVrlJubG13/rLPOqpa/V69eKikp0fbt260N30RZv369jDF68803NWXKFJ199tl6+OGHnXkKCwu1Zs2aOm2/Q4cO9S5TIBDwlAYAQHNAoxsAgP/q06eP+vTpI0kqLy/Xz3/+c/3617/WPffcU21CtTZt2lTLl5mZKUnav39/0su4bt06SdLHH3+sAQMG6MUXX9TmzZtVUFBgzdOqVSsdf/zxddp+fYeXt2nTJmZv9ldffSVJMXvBAQBoThheDgBADOnp6Zo8ebKkyueSG4uioiK1bdtWa9as0SOPPKKysjLdfvvtzjzJHF5+7LHH6v3331dFRUW15e+++64kqWfPnvXaHgAAfkNPNwCg2du6dWt0ErMDvf/++5K8Dbmuq/r2kq9bt04nnHCC2rRpozZt2uhHP/qRfve732nixInRycu+LZnDy0eOHKnHHntMixcv1qhRo6LLn3jiCXXo0EF9+/at1/YAAPAbGt0AgGbvtNNOU8eOHTVixAh1795dkUhEGzZs0K9+9Su1atVK119/fdL2feyxx0qSHnjgAY0ZM0bp6enq1q2bWrduXWPdffv26aOPPtL5558fXTZt2jQtXLhQN998s5YuXRpzH61bt44Om0+04cOH6/vf/76uueYaFRcX68gjj9TTTz+tl156SU8++SQxugEAzR7DywEAzd5tt92mQw45RL/+9a911llnafjw4XrwwQd16qmn6p133ok2jJPhpJNO0qRJk/T8889r0KBBOuGEE1RUVBRz3Q0bNigSiUTDhUlS586ddc011+jFF1/Uq6++mrRyujz77LMaPXq07rjjDp1++ul6++239fTTT+uSSy5JSXkAAGhMAsYW3wQAAAAAAMSFnm4AAAAAAJKERjcAAAAAAElCoxsAAAAAgCSh0Q0AAAAAQJLQ6AYAAAAAIElodAMAAAAAkCQ0ugEAAAAASBIa3QAAAAAAJAmNbgAAAAAAkoRGNwAAAAAASUKjGwAAAACAJKHRDQAAAABAktDoBgAAAAAgSWh0AwAAAACQJDS6AQAAAABIEhrdAAAAAAAkCY1uAAAAAACShEY3AAAAAABJQqMbAAAAAIAkodENAAAAAECS0OgGAAAAACBJaHQDAAAAAJAkNLoBAAAAAEgSGt0AAAAAACQJjW4AAAAAAJKERjcAAAAAAElCoxsAAAAAgCSh0Y16mz9/vgKBQLVX27ZtddJJJ+nPf/5zzHU/++yzlJXTy75XrVqlKVOmaNeuXUkpU9UrLS1NHTt21OWXX64tW7ZY18vKylJ+fr6GDh2qGTNmaPv27bVu+8DXjTfemNDjiMe0adN09NFHKxKJ1EgrLi7WjTfeqIKCAmVlZenEE0/U6tWrE16GhtpPXcydO1eHHXaY9u3bl5L9AwAAILlodMOzefPmafXq1Vq1apXmzJmjUCikESNG6Pnnn4+u84Mf/ECrV69W+/btG7x88ex71apVmjp1asIb3VWqzt3y5ct19dVX6+mnn9bgwYNrNLwOXO/hhx/W8ccfr7vvvls9evTQX/7yF+e2D3xdd911STmO+vriiy90zz33aNq0aQoGq3/87NixQwMHDtTKlSs1c+ZMLVmyROFwWGeeeaa+/vrrhJWhofZTV2PGjNFBBx2ke+65p8H3DQAAgAZggHqaN2+ekWTWrFlTbfk333xjMjMzzUUXXZSikv3Pvn374sp/7733Gklm48aNiSnQf9nO3e23324kmSeffNK5njHGfP7556agoMC0bt3abNu2rdZtNyb/93//Zw477DATDodrpP3gBz8wxxxzTLVr98477xhJZt68eQkrQ0Ptpz7uu+8+k5OTE/d9C6BxqPo8rnqFQiFz2GGHmcsuu8z8+9//bpAyTJ482STza95f//pXM3nyZPP1118nfNsLFy40Rx99tMnKyjKSzPr162OuV9fz/O31MjMzTV5enjnppJPM9OnTzX/+859at33g64Ybbkj4Mcdj6tSppkePHjHr1t27d5sbbrjBdOzY0WRmZpoTTjjBrFq1qs7b/u1vf2s6dOhg9u7dm8gixy2Zx5wojfXcITXo6UbCZGVlKSMjQ+np6dFl3x7i/cc//lGBQECvvPJKjfyzZ89WIBDQ3//+d33yySe6/PLL9Z3vfEctW7bUYYcdphEjRujdd9+tkW/KlCkKBAJat26dzj//fB1yyCE64ogjYg4vr8t2p0yZoptuukmS1LVr1+gQ7RUrVkTX+fjjj3XxxRerXbt2yszMVI8ePfTwww97Pnf9+vWTJH3++ee1rtupUyf96le/0p49e/Too4963ue3jRgxQn369NFjjz2m4447Ti1atFBBQYEmT54ccyh4fZWVlWnu3Lm6+OKLa/Ryv/rqq3rhhRd0//33q2XLltHlhx9+uCTp008/jXv/DbmfKj/84Q/VqVOn6P/79u3TqFGj1LFjR73zzjvR5ZdccomKi4u1cOHChO4fQGrVdVRTU5SsEWFffvmlRo8erSOOOEIvvfSSVq9eraOOOsqZp7mOHpOSP4KsMY7Gagyj5uqiMZ47pE5aqguApiscDquiokLGGP3nP//Rvffeq3379uniiy+25jnzzDPVrl07zZs3T6ecckq1tPnz5+u73/2uevXqpddff11t2rTRXXfdpbZt2+qrr77SE088ob59+2r9+vXq1q1bjW2fe+65uvDCCzV27Fjt27cv5ofrF198Uet2r7rqKn311Vf6zW9+o2effTY6PP3oo4+WJL333nsaMGBAtPGbn5+vl19+Wdddd5127NihyZMn1/tcfvLJJ5Kktm3b1mn9M844Q6FQSK+//nqNtKrrcqC0tNrf6kVFRSouLtavf/1r3XLLLcrLy9Pjjz+uadOmqaCgQFdddVWdymbz9ttva+fOnRo6dGiNtDlz5qhLly4aOnRotbIXFxdLUrUfcuLRUPupsm7dOn33u9+VVNmgHzlypLKzs1VUVKS8vLzoevn5+erevbteeOEFXXHFFQktA4DU6dmzp/r06SNJGjp0qMLhsH7xi1/oj3/8oy655JKYeb755ptqPwo2Nx999JHKy8v1ox/9SEOGDKlTnrqe5wPXk6TzzjtPEyZM0KBBg3Tuuefq448/rvbZHCtPY/PAAw/o4IMP1rnnnlsj7bLLLpMxRitXrozeU7m5uTrxxBP1pz/9SZdddlmt209LS9NPfvIT/eIXv9DPf/7zRnFvJvuYE6UxnjukUIp72tEE2YZcZWZmmlmzZsVc98Bh2hMnTjQtWrQwu3btii577733jCTzm9/8JuY+KyoqTFlZmfnOd75jJkyYUC2tagjdHXfcUeu+67pd1/Dy0047zXTs2NHs3r272vKf/vSnJisry3z11VfW/VWV6a233jLl5eVmz5495s9//rNp27ZtteHidRkqnpeXZ3r06FFj27Fe5eXl1u0YY8y///1vI8kcfvjh1a5LWVmZyc/PN2eeeaYzf13cfffdRlK1IfHGGBMOh83BBx9sLbsk87vf/c4YY8ysWbNM7969TVpampk8eXK99l/X/ZSUlJjLLrvMdOzY0bRu3dr07dvX/PWvf6338e7atcsEAgEzbdo08/LLL5tDDz3UjBs3zpSVlcVc/5JLLjF5eXn13g+Axsf2Gf7CCy8YSebOO+80xvyv/ioqKjLnnXeeOfjgg01+fr4xxpg33njDnHzyyaZVq1amRYsWpn///ubPf/5zzP39+c9/Nscdd5zJyMgwXbp0Mffee2+N4eVjxowxnTt3rpHXNgz9/fffNxdeeKFp166dycjIMAUFBWb06NGmpKQkmufbr9dee815Xmo7pjFjxtTY5pAhQ6zbq+t5rq1O/X//7/8ZSWbq1Km1bvvbtm/fbq6++mrTsWNHk5GRYXJzc82AAQPM8uXLnfmMMebMM880hYWFZs6cOaZXr14mKyvLdOzY0dxxxx0xh01/W2lpqWnTpo256aabaqS98sorRpJ5+eWXqy3fsWOHkWRuv/32WrdfZevWrSYQCJi5c+fWOU8s8R6vMQ13zLW54IILTEFBQfT/vXv3mh/+8IfmsMMOM2+//XZ0eaLOHZo+hpfDswULFmjNmjVas2aNXnzxRY0ZM0bXXnutHnroIWe+K664Qvv379eiRYuiy+bNm6fMzMxoL3lFRYWmT5+uo48+WhkZGUpLS1NGRoY+/vhjvf/++zG3e95559VaZi/bPVBJSYleeeUVjRw5Ui1btlRFRUX0dcYZZ6ikpERvvfVWrdvp16+f0tPT1bp1a5155pnKz8/Xiy++WOMXdhdjTMzlB16XqldtPd1r1qyRVDm0PicnJ7o8PT1dRx55pHbs2FHnctl88cUXCgQCys3Nrbb8ww8/1K5du/SLX/yiRrnHjBkjSTrxxBMlSe3bt9fUqVN1zjnn1Hv/dd1PRUWFunbtqr/+9a/atWuXrrnmGp111ln65ptv6rW/9evXyxijN998U8OHD9eQIUP08MMPW3vT27Vrp+3bt9cYpQDAP2yjms4991wdeeSR+sMf/qBHHnlEK1eu1Mknn6zdu3dr7ty5evrpp9W6dWuNGDGiWt0pSa+88orOPvtstW7dWgsXLtS9996r//f//p/mzZvnuZx/+9vfdMIJJ+itt97StGnT9OKLL2rGjBkqLS1VWVmZrrrqKv3sZz+TJD377LPRYddVI3tiqcsx3X777dFHtaZPn67Vq1dr1qxZ9S5/MkaPHfg60OjRo/XHP/5Rd9xxh5YtW6bf/va3OvXUU7Vz585a91tUVKQPPvhAv/71r3XTTTfpueee06BBgzRt2jQ9/vjjteavzwiyqpeXkV0HjsaKR7zHKzXcMdfm2yPZBgwYoC+++EJFRUXR7yxS4s4dfCDVrX40Pa5ff0877TTTokWL6MQqtt7mE044wfTr188YU9nb3L59e/PDH/4wmv6zn/3MBINBM2nSJPPSSy+Zt99+26xZs8Ycd9xxNX71rvrFffv27THLeeC+67pdW093VY+w67VgwYJaz92CBQvMmjVrzPr1680XX3xhXc/2C/vevXtNKBQyp5xySp3zuNx6660mPT3d7N+/v0ba4Ycfbi644ILo/+PGjTNXXHGFMaay9/iss84yP/vZz8zXX39tgsGgKS4ujq77hz/8wQwcONAYY8yPf/xjk5GRUWP7S5cuNZLMsmXLaqQVFhaaI444osbyK6+8st493V72U+WQQw4xGzZsqNf+fvWrXxlJpmvXrmbQoEEmKyvLbNq0ybr+pEmTjCSzZ8+eeu0HQONT11FNtpFa/fr1M+3atav2eVBRUWF69uxpOnbsaCKRSHR53759TYcOHap9fhcXF5tDDz3Uc0/3ySefbA4++OAa9eqB6jvhaF2P6bXXXjOSzB/+8Idat9kYRo+1atXKjB8/vk7n4ECJGGHWkCPIahuNtXr1aiPJuo1EjaiL95gTMZqNkWzwgme6kVC9evXSyy+/rI8++qjaL33fdvnll2vcuHF6//339emnn2rr1q26/PLLo+lPPvmkLr30Uk2fPr1avh07dujggw+Ouc1AIFBr+bxs90CHHHKIQqGQRo8erWuvvTbmOl27dq11Oz169IjrGbEXXnhB4XBYJ510kudtHGjt2rXKzc1VVlZWteVvv/22Pv30U91+++3RZZMmTVKPHj00efJkPfTQQwqHw/r1r3+tUCikww8/XH/72980aNAghcNh3XHHHZo9e7akymeqysrKtG/fPh100EHR7ZWXl0uSQqFQtX1v2LBBRUVFuvvuuxNyjF7388EHH2j//v064ogj6rW/oqIitW3bVmvWrNG2bdvUq1cv3X777Zo/f37M9b/66itlZmaqVatW9doPgMarapLMKscee6xmz55dY1TTgSO19u3bp7ffflvXXHNNtc+Dqrrn5z//uT788EN1795d+/bt05o1azRu3Lhqn99VPchPPPFEvcv8zTffaOXKlbryyivr3FNcm/ockxd1Pc8uxjF6rEePHtWWHTh67MQTT9T8+fPVpk0bnXrqqSosLKxTj2oiRpjVZQTZ6aefXi3toYce0hNPPFFjBNmCBQuc+zpwNFZd5on5tkSNqIv3mA8czdaxY0f97ne/01lnnaVNmzbV+ZnrA0eyTZkyRWeffbZzMt14zx38gSuPhNqwYYOk2od0XXTRRZo4caLmz5+vTz/9VIcddpiGDRsWTQ8EAsrMzKyW54UXXtCWLVt05JFHei5fXbdbtc7+/furrduyZUsNHTpU69evV69evZSRkeG5LF5t2rRJN954o3JycvSTn/wkIdtcu3atdu/erV27dkV/fAiHw/r5z3+uLl26VJscr2PHjrr00kt11llnSZLefPPNaEO2sLBQGzZs0KBBg7RgwQIVFBREJ8Kp+jL1r3/9S7169Ypur2rm8HfffVcnn3yypMrHAK677jp17dpVP/3pTxNyjF72880332j06NG67bbb6t0YXrdunU444QS1adNGbdq00Y9+9CP97ne/08SJE6sdf5VPP/00OlkfAH+oarClpaUpLy8vOjHntx24/Ouvv5YxJua6HTp0kKTo0OWvv/5akUhE+fn5NdaNtawuvv76a4XDYXXs2NFTfts263pMXtT1PNvs27dPO3fu1LHHHlsjrbYfyRctWqRf/vKX+u1vf6vbb79drVq10siRI3XPPfc4r8HatWuVnp6uCy64oEbaF198ocLCQknStddeq5KSEs2dO1eRSEQjR45U586d9eCDD2r//v1KT0+v8WNyVdSWvn371ij7P/7xDx1xxBHRGeGrHtf605/+ZC2rVBmhxhijkpKSmPVhnz599OWXX1obrnU93oY45jvuuCOaNmbMGE2YMEEff/yxjjvuOOc5qLJu3TpJlZFsBgwYoBdffFGbN29WQUFBzPVrO3doHmh0w7N//OMf0Webdu7cqWeffVbLly/XyJEja+3tPfjggzVy5EjNnz9fu3bt0o033lgt7MOZZ56p+fPnq3v37urVq5eKiop07733xv0loK7brap4H3jgAY0ZM0bp6enq1q2bWrdurQceeECDBg3S4MGDdc0116hLly7as2ePPvnkEz3//PN69dVX4yrjgarOcUVFhbZv36433nhD8+bNUygU0pIlSxLSC7Fx40bt3LlTnTp10gUXXKAbbrhBJSUlevDBB1VUVKQVK1bU+HHh+OOP16xZs7Rq1apqFUhVo7u0tFRTp07VM888E02r6pV/6623qjU6e/bsqcLCQv3yl79UXl6ecnJy9Ktf/UrvvfeeXnnllXrP9hkIBDRkyJBqId687Ke8vFw//OEPdfTRR+uWW26p836kyi9wH330kc4///zosmnTpmnhwoW6+eabtXTp0mrrRyIRvfPOO7ryyivrdawAGre6jmo6cKTWIYccomAwqK1bt9ZY74svvpCkaC/fIYccokAgoG3bttVY99vLsrKyVFpaWmO9b/cwHnrooQqFQvr3v/9da7nrqj7H5EUqR4/l5uZq5syZmjlzpjZt2qTnnntON998s7Zv366XXnrJmq+uI8xso8uq9t1QI8hqG42VlpbmvIaJGFEnJf6YvYxmYyQbPEnl2HY0TbGec8rJyTHHH3+8uf/++01JSUmNdWM987Vs2bJo/o8++qha2tdff22uvPJK065dO9OyZUszaNAg88Ybb5ghQ4ZYn+n+8ssvY5bzwH3XZ7uTJk0yHTp0MMFgsMasrBs3bjRXXHGFOeyww0x6erpp27atGTBggPnlL39Zp3NX23PX3z7HGRkZpl27dmbIkCFm+vTpMZ+z8/pMd9WsratWrTKjR4822dnZpnXr1ubss8827733Xo313377bXPYYYeZCy64wPzkJz+plvbKK6+YwsJCM3PmTHPuuefWyDt48GBzxhln1Fj+2WefmdNOO820bNnSHHrooeaSSy5xPidoe6Z7z549RpK58MILY+ar637C4bC58MILzVlnnRVz5vfa9vPmm28aSebZZ5+ttvz66683kswrr7xSbXnVjKtFRUWWIwbQlNT189hWf/Xv39/k5+ebb775JrosHA6bY4891vMz3TNmzDDBYLDas7ClpaXmyCOPjPlM9yGHHFKjXAd68MEHjaSY9UQsdT0mL89017VOjbXe559/bgoKCkxOTk61ujWeeVLOOecc07ZtW+c6bdq0MWlpadE5cIypfMZ9yJAhpkuXLqa0tDS6fNy4cea4444zxx13XLVn4hcsWGAkmb/97W/Vtv3uu+8aSWbmzJnRZeXl5Wbw4MGma9euZt++fTXKU9tcKd///vdN7969ncfkUp/jNaZhjnnfvn2mT58+tX53+7bu3btX+y5z6aWXmmAwWKNMVeI9d/AHGt1AM3fTTTeZgw46yFRUVNS6btWXk9dee8188cUXpnXr1uazzz6Lpn/99demRYsWJj8/3/zzn/+skf+ZZ54xoVDI/Pvf//ZU1vLycrN//35z2WWXmVtvvdXs37+/WrlfeOEFEwgEzN///ndP269y1VVXmSFDhsScWC6R+6nyox/9yAwYMCAh2wKQevE2ulesWGHS09NN3759zR/+8Afzpz/9yZx22mkmEAiYhQsXVlt32bJlJhgMmkGDBpklS5aYZ555xpxwwgmmoKCgWmP6008/Nenp6eakk04yL7zwglm8eLEZMmSI6dq1a41G94YNG0yrVq3M4YcfbubMmWNeffVV8/TTT5uLLrooOllmVeP4Jz/5iVm1apVZs2ZNtYk0v62ux5TMRve8efPM6tWrzRtvvGEWL15sxo8fb3Jycsyhhx5qXn311Xpve9euXaZ3797m3nvvNc8//7xZsWKFuffee01WVpa5+OKLrfk+/fRTI8l06tTJnHrqqebFF180S5YsMUOHDjWtWrUya9eurbb+nDlzoj+OH2jTpk1Gknn00Udr7KOwsNDk5uaap59+2ixdutSccsoppk2bNtZJQV2N7nA4bHJycszEiROtx+RS3+M1JvnHXFZWZn7wgx+YSy+9tNqPWFVkCVe3d+9eEwwGzW233RZd9tlnn5mMjAwzfPjwGuvHe+7gHzS6gWZu6NChZvDgwbWuV1xcbI499ljz29/+NrrsmmuuMVdddVW19Y488kgzevTomNuIRCKmX79+5tprr/VU1lixYefNmxdNv/HGG81FF13kadtVPvvsMyPJZGVlmYMOOij6ev311xO6nyqffPKJSU9PN2+88UZCtgcg9eJtdBvzv5jWBx10kGnRooXp16+fef7552Nu57nnnjO9evUyGRkZplOnTuauu+6KOSv50qVLzfHHH29atGhhDj/8cPPQQw9Z43S/99575oILLjBt2rSJbveyyy6rNprNNSIslrocUzIb3YkePVZSUmLGjh1revXqZbKzs02LFi1Mt27dzOTJk2P2rFapzwgz1+gyY5I/gsyY+EdjJXJEnTHxH3M8o9kYyQavaHQDzVgkEjE5OTlmwoQJCdnenj17TH5+vvn000+t67z77rvmzjvvNOFwOCH7bOpeffXVmL/YAwD8qa4jzGobXWZM8keQGRP/aKxEjqgzJv5jbsjRbIxkQ5WAMZYYCQBQTxMmTJCk6IQnAACgupNPPlkVFRV6/fXXrevs2bNHAwcO1PXXXx+dZHPcuHEqLy/XY489Fl3PGKMBAwaosLBQDz30UL3LMmXKFE2dOrXasnnz5umyyy6TVBlxpEePHnr11Vc1aNCgem9fqtvxSg1zzJ9//rm6dOmirKysapOuvfjiixo8eLAk6aabbtKWLVv01FNP1Wvb35aIcwf/oNENIG4bNmzQkCFD1LdvXy1ZsqTajKIAAKCSMUaHHHKIrrjiCt1///0J2eY//vGP6KzpB0aCSYTXXntNH3/8sX784x97yp+M45WSe8yJEu+5g7/Q6AYA+FJJSYnKysri3k5GRkaNMDcAAMAtEfWwX+rgxvnTUB28/vrrGjFihDp06KBAIKA//vGPzvVXrFihQCBQ4/XBBx80TIEBAA2mpKREXTu3Uk5OTtyvrl27qqSkJNWH1OhQDwMAbBJVD/ulDk5LdQG82rdvn4477jhdfvnlOu+88+qc78MPP1R2dnb0/7Zt2yajeACAFCorK9O27WF9XtRF2a29/75cvCeizoWfqayszBe/tCcS9TAAwCYR9bCf6uAm2+gePny4hg8fXu987dq108EHH5z4AgEAGp1WrQNq1TrgOX9E3vP6HfUwAKA28dTDfqqDm2yj26vevXurpKRERx99tG677TYNHTrUum5paalKS0uj/0ciEX311Vdq06aNAgH/3AQA0BgYY7Rnzx516NAhYRPjhE1E4ThmLgmbSELKgf+hHgaAxqmx1cN+qoObTaO7ffv2mjNnjgoLC1VaWqrf/e53OuWUU7RixQp973vfi5lnxowZNcIoAACSa/PmzerYsWOqi4EEox4GgKaBejjxfDF7eSAQ0JIlS3TOOefUK9+IESMUCAT03HPPxUz/9i/su3fvVqdOnTRIZyhN6fEUGQCarX89cnzM5ZH9pdoy4S7t2rVLOTk5ce2juLhYOTk52vZhp7if6c7vtkm7d++u9hwyqmss9XCwhf2Zv4DjecBAZmbshMwMax5l2L8HRLLs+UyG/X6MZITsaemONNc20+wjAiLpjjRLPlceYy+iIo40E0rCNr2+7S1FMY6BFQGP36Q9b9Pj/gKOTsNg2JHRki9YYS+Ia3sBR1qw3LFN1/685iuzn5RQaeyCBsrtBxAsrbCmufKp1DHDtyPNHPD5WCPNMflYpCT2NitMud7UnxtNPeynOrjZ9HTH0q9fPz355JPW9MzMTGXGqIjTlK60AI1uAPDC1TCSlNBhwxFFbN8X65wfyZPoejgYsDd2A0EPaUFLY1ySQo5Gd8jR6E5zNJ49pzka3a6GdYIb3RHHt8pAEhrdzm26vuO7PmL83Oh2NXa9NLqD3hrdQXu7VEHHwQUdJ8WZz5UWcTS6w5ZGd8TR6A6VW9Nc+RR03AyOe9k4roFx/MoScd1gpvHUw36qg5t1o3v9+vVq3759qosBAEiSsDEKxzGgK568qB31MAD4Wzz1sJ/q4Cbb6N67d68++eST6P8bN27Uhg0bdOihh6pTp06aNGmStmzZogULFkiSZs6cqS5duuiYY45RWVmZnnzySS1evFiLFy9O1SEAANBkUQ8DAFA3TbbRvXbt2moznk6cOFGSNGbMGM2fP19bt27Vpk2boullZWW68cYbtWXLFrVo0ULHHHOMXnjhBZ1xxhkNXnYAQMOIyCjidSzmf/MjNuphAEBt4qmH/VQH+2IitYZSNSHASTqbZ7oBwOFfv+9tTTvikvUxl1eYcq3QnxIyYUrV5/XGD9qrdRwTqe3ZE1HX7lt9MYmLH1Rd15Mzf6i0GM9vB1wTqbnmErBNpOacEM3ebxFp4Xje2zVZmmNCtHC6awI213Pbjm065omzPbvtmrwsOZOsOdKcz7p6S7M+7+16xNXrN2nXNh2Psnp9htz1TLdrkjVbWtD++LJ70jbnhGiOfI7yh0o9TqRW6ppILXZa0DWRWokjrcwxyZojTfvtE6KpzH7CjCOfbQK2ClOmV/cvajT1sJ/q4Cbb0w0AQG3o6QYAIHXo6a6UmKjnAAAAAACgBnq6AQC+xezlAACkDrOXV6LRDQDwrYicj0bWKT8AAPAmnnrYT3Uww8sBAAAAAEgSeroBAL4VllE4jolY4skLAEBzF0897Kc6mEY3AMCzzc8cG3P5EefHDgvW0MKm8hVPfjQ+gRZZCsQKGdayhT1TliUsmCSTGTt2lsmyf01yhQwLt3CkOcKCRTJdIcMcYcEcIcOc+RzRT60hwxzfHF3bc4Xp8hwyzGOaK1SXM5yYF67PEI9hyJISMsxDODGvIcMCFfYDD7m26Yiq5bqHgo58oZD9gpu02OUMlTpC4wUdaWn2fQVD9nzOWzJkP3DX7SVLOQORoLTflbH+4qmH/VQH0+gGAPgWz3QDAJA6PNNdiWe6AQAAAABIEnq6AQC+FVFAYfcgu1rzAwAAb+Kph/1UB9PoBgD4VsRUvuLJDwAAvImnHvZTHUyjGwDgW+E4e7rjyQsAQHMXTz3spzqYZ7oBAAAAAEgSeroBAE7bn+tuTSs4690GLEn90dPtT4GMDAWCMcJ8ZcQO/SXZw4JJ9tBgkUx7DKxIpj1UT0WWPc0Z3ssVTsyZz5oUR8iw2Mtdobic23N84/QcFszRdeTM53pbB2OPZ3XlcYbw8prRlc/jkNtggkOGuc6xc3ser7cr9JcrVJcrnwIero/r0rjuLde+XBxTeDt7T8P2i2ArSSCS+DqPnu5KNLoBAL4VMQFFnN+Cas8PAAC8iace9lMdzPByAAAAAACShJ5uAIBvMbwcAIDUYXh5JRrdAADfCiuocByDuhyPJQIAgFrEUw/7qQ6m0Q0A8C0T5zPdxkfPkwEA0NDiqYf9VAfzTDcAAAAAAElCTzcAQHtfOsKa1u70DxqwJImVime6t2zZop///Od68cUXtX//fh111FGaO3euCgsLPZcD35KVIQUzayw2LWoui6ZZwoJJUiQrdqwrV1iwsCsty96nEc50hf7ylhZxhAxzhfEKewkZ5vjm6NqXM9SYK4RUmj0+lmubttBfUm1hnSx5HNtzbTBgvJXDlc9ryLBI2FFODyHDgmWO7TnCXAUcIbxCZfa0iCuf6/6qsJfTGXbOkmaC9kwhR+gyV1gzVz4nR/mdPasBS6rjunnFM92VaHQDAHwrbIIKu75V1Zq/fut//fXXGjhwoIYOHaoXX3xR7dq107/+9S8dfPDBnssAAEBTFU89XN86uDGj0Q0A8K2IAorE8SRVpJ5dSnfffbcKCgo0b9686LIuXbp43j8AAE1ZPPVwfevgxoxnugEAqEVxcXG1V2lpacz1nnvuOfXp00cXXHCB2rVrp969e+uxxx5r4NICAIDGhEY3AMC3qp4li+clSQUFBcrJyYm+ZsyYEXN/n376qWbPnq3vfOc7evnllzV27Fhdd911WrBgQUMeNgAAjUIi6mA/YHg5AMC34n+mu3Jo2+bNm5WdnR1dnpkZe8KuSCSiPn36aPr06ZKk3r1765///Kdmz56tSy+91HM5AABoiuJ7pts/w8tpdAMAfKvyWTLvv5RX5c3Ozq7W6LZp3769jj766GrLevToocWLF3suAwAATVU89XA89XdjQ6MbAJqLVztak1qd/K8GLIh/DRw4UB9++GG1ZR999JE6d+6cohL5VGamFIoRMswVFizTHs/KFhqsIssehyiS6QgLluUt9FeFI5xYUsKCedimO2SYvVcq4vrGGXLkc4UFc+RzpTnDf1kuQcDx3d9rdC/XNiOu0E3OmGeO/TlCZ8kVTsxSFlfINlcIsmC5I6yWY5vBcnuaqyPVEeHLzXKBXKffVY6QLUxXbcVwvgkc+RxTf1sPwU/ThTcyNLoBAL4VUVDhBpy9fMKECRowYICmT5+uH/7wh3rnnXc0Z84czZkzx3MZAABoquKph/00ezmNbgCAbyXqme66OuGEE7RkyRJNmjRJ06ZNU9euXTVz5kxdcsklnssAAEBTxTPdlWh0AwCQQGeeeabOPPPMVBcDAAA0EjS6AQC+FVFQkQYcXg4AAP4nnnrYT3UwjW4AgG+FTUBhj5MOVeUHAADexFMP+6kOptENAPCtcJwTqYV99Cs7AAANLZ562E91MI1uAPCRVm+0s6btHfzvBiwJkDwmI00mVPMrjMlwhQyzh90JZ8T+QugMC+Yx9JcrnyuEl+fQX15DjVnymTRHeK8MR5guZ3gve5JJs8fOCri26QgLFvQSMsyRx0Q8hvAKOLbp6OHzuj+lO7bpCidm2V/YEYvLFmZMqiUsWJmjjK52m+uUeP/d1cPOPG7RcXDhiCsmnSMsWIX98zBoyWeC3sKToXY0ugEAvhUxQUXimL084qOZUwEAaGjx1MN+qoNpdAMAfIvh5QAApA7DyyvR6AYA+FZE8U3E4hghCQAAahFPPeynOjjhTzkAAAAAAIBK9HQDAHwr/jjd/DYNAIBX8cXp9k8dTKMbAOBbYRNUOI6J1OLJCwBAcxdPPeynOphGNwA0Mfmrc6xp2/pvb8CSAKlhMkIxQ4ZFMuzhbiKWsGCSPTSYK7xX2GNYsHCmNckdMiwJYcFcIb5s24w4QoYpw/EEpiufI/RXMGTfZtBjPlf4r6AljJfn8F7WFPu+JCni2qbr+VjHDsNhx3ugwp5mC1HmDAMXdrwHHKHGXOHEAuX2NAUc58sVks7Lo8bOPB7DxzneOoGIIzSbK/qdK9SYRSQcrnce1A2NbgCAb0UUUCSOmKrx5AUAoLmLpx72Ux1MoxsA4FsMLwcAIHUYXl6JRjcAwLfij9PtnwofAICGFl+cbv/Uwf45EgAAAAAAGpkm2+h+/fXXNWLECHXo0EGBQEB//OMfa82zcuVKFRYWKisrS4cffrgeeeSR5BcUAJAyEROI+4XYqIcBALWhDq7UZBvd+/bt03HHHaeHHnqoTutv3LhRZ5xxhgYPHqz169frlltu0XXXXafFixcnuaQAgFSJ/HdYm9eXn2KEJhr1MACgNvHUw36qg5vsM93Dhw/X8OHD67z+I488ok6dOmnmzJmSpB49emjt2rW67777dN555yWplADgzXfW2uMKfdxndwOWpGmLmKAicUzEEk9ev0tlPRxJDymSVjMOUDjTHhsobAkLJklhSzgxd1gwe/mcYcEcIbySE07MFRbMEQYrPXaaSXeE4nKkBdO8pYVcaUF7Wpor1JgjZJhtm0FHLC7XDMuu8F4hR5wo1wRS7nBi1iRVhO3vjwpXODFLWkXQvj3jCBnmCjUWKXOExwo6ej1dUdTKPYbxqn/ELXeMOEch3aG/HPWQK1+F/frYbj3jyONVPPWwn+pg/xxJLVavXq1hw4ZVW3baaadp7dq1Ki+PHfivtLRUxcXF1V4AAKD+qIcBAA1h1qxZ6tq1q7KyslRYWKg33njDuu7WrVt18cUXq1u3bgoGgxo/frxz2wsXLlQgENA555xTrzI1m0b3tm3blJeXV21ZXl6eKioqtGPHjph5ZsyYoZycnOiroKCgIYoKAEiQsAJxv5AY1MMA0Pw0dB28aNEijR8/XrfeeqvWr1+vwYMHa/jw4dq0aVPM9UtLS9W2bVvdeuutOu6445zb/vzzz3XjjTdq8ODB9S5Xs2l0S1IgUP3Cmf+Owfn28iqTJk3S7t27o6/NmzcnvYwAgMSpGtYWzwuJQz0MAM1LQ9fB999/v6688kpdddVV6tGjh2bOnKmCggLNnj075vpdunTRAw88oEsvvVQ5OTnW7YbDYV1yySWaOnWqDj/88HqXq8k+011f+fn52rZtW7Vl27dvV1pamtq0aRMzT2ZmpjIzHQ9YAQCAOqEeBgB48e1Hi2x1Q1lZmYqKinTzzTdXWz5s2DCtWrUqrjJMmzZNbdu21ZVXXukcrm7TbH7C79+/v5YvX15t2bJly9SnTx+lpztmNQEANFlhxTu0DYlCPQwAzU989XClgoKCao8azZgxI+a+duzYoXA4HPNRpm//6Fsff/3rXzV37lw99thjnrfRZHu69+7dq08++ST6/8aNG7VhwwYdeuih6tSpkyZNmqQtW7ZowYIFkqSxY8fqoYce0sSJE3X11Vdr9erVmjt3rp5++ulUHQIAIMmYvTx5qIcBALVJxOzlmzdvVnZ2dnR5bSOgYj3KZHuMqTZ79uzRj370Iz322GPKzc31tA2pCTe6165dq6FDh0b/nzhxoiRpzJgxmj9/vrZu3VrtgfmuXbtq6dKlmjBhgh5++GF16NBBDz74IOHCAKTMiRvs/ajvHF/agCXxr7AJOkPv1CU/YktlPRzJjB0yLJLuCvHlSLOEBqtwhAxzhfByhvdyfFf0HDIss/6hvyTJZNhDVinTEjrLEcIrLcP+mRZyhPBKT7Pnc6VlhOxpaa40R6iugCV2U5ojPFmFK6STQ9ARJ8oVFszr51JZhf1rf5kjnFg4ErssJSH7CBVbmDFJqihzhBpzhHMzIUdYs4A9zTijYNW/Iea4NN45Nuq4Xd35Kup/n4RDiQ8ZFk89XJUvOzu7WqPbJjc3V6FQKOajTN/u/a6rf/3rX/rss880YsSI6LJIpPKipKWl6cMPP9QRRxxR63aabKP7pJNOik7AEsv8+fNrLBsyZIjWrVuXxFIBANA8UA8DABqTjIwMFRYWavny5Ro5cmR0+fLly3X22Wd72mb37t317rvvVlt22223ac+ePXrggQfqHFWjyTa6AQCojVFAkTjCfhlChgEA4Fk89bCXOnjixIkaPXq0+vTpo/79+2vOnDnatGmTxo4dK0k1Hn2SpA0bNkiqfGzqyy+/1IYNG5SRkaGjjz5aWVlZ6tmzZ7V9HHzwwZJUY7kLjW4AgG8xvBwAgNRJxPDy+hg1apR27typadOmaevWrerZs6eWLl2qzp07S1KNR58kqXfv3tG/i4qK9NRTT6lz58767LPPPJU7FhrdAADfipiA89nIuuQHAADexFMPe803btw4jRs3LmZarEefXI9K1XUbteEnfAAAAAAAkoSebgBIou//Y681bXnPVg1YkuYprKDCcfy+HE9eJE84I6hAWs1rE86yXy/bDOWSVGGZNdzzLORZjjSP24w4ZiiPOGYhNxn2fAHXbOOZsdPS0u15MtMrrGleZyHPSiv3li9kL4trJvKgbLOX2/flCofk6qlzbbMiYp9FusLjUN2SsP1rf4ljZvNyS1nSHDPSl1fYy18WcuzLkRYOOd4Djg7RQLmrt9R1Luvfy+qYkN4zr7OXBx0zyNvKGQkmvs6Lpx72Ux1MoxsA4FsMLwcAIHVSMby8MaLRDQDwrYiCisTxS3k8eQEAaO7iqYf9VAf750gAAAAAAGhk6OkGAPhW2AQUjmN4Wjx5AQBo7uKph/1UB9PoBgD4Fs90AwCQOjzTXYnh5QAAAAAAJAk93QAQp5Hv77CmLemR24AlwbcZE3SG86lLfjQ+Ji0ok17z2kRC9l6RSFr90yLp9jJEHN+gXGnGlZZujzdk0hyxiBz5Ao5wYiFHmi00mCssWJYzzR76K9MR3ssV+suVluEKGeaIwZRuCeNlCyUmSREPoaXi2aYthJdUS4gyx3G70ryEKAt5jJ3lzBWwH7drGLJx9DGasOMaWN7/gbB9XwHHZ4Ycob8cUexq+exy5bOnBdItn3ke72WXeOphP9XBNLoBAL4VVkDhOL5ExJMXAIDmLp562E91MI1uAIBvRUx8z4RFvHXWAAAAxVcP+6kO9k+fPQAAAAAAjQw93QAA34rE+Ux3PHkBAGju4qmH/VQH++dIAAD4logCcb/qY8qUKQoEAtVe+fn5STo6AAAat4asgxszeroBAL4VNgHnrLZ1yV9fxxxzjP7yl79E/w+F7DPuAgDgZ/HUw/HU340NjW4AqKPLP9oUc/m8ozo1cEnQmKWlpdG7nWTh9EDMkDfhTPsXtHCGI+xOhm0/9jLY8tSWFs50hCjKcKRl2WMKBTJih7mSpFCmPS0jwx5WK9OS1sIR+qtVRqk1zWvor5ZpZda0FiF7WmbQvs10R3ymtEDs85VuWS5J5cbbD2shRwypsGMwaoVjf65Gyn7HDb0/bL9pyywhylwhz8rS7GVMD9n3FQzat1nqCENmvxOksCPUmHFM1GUd2uya3MvVSHTkCztChjluPYUj9v1Zot9VbtOSz089y40NjW4AgG8l6pnu4uLiasszMzOVmZkZM8/HH3+sDh06KDMzU3379tX06dN1+OGHey4DAABNFc90V/LPkQAA8C0RBRQxcbz++6t/QUGBcnJyoq8ZM2bE3F/fvn21YMECvfzyy3rssce0bds2DRgwQDt37mzIwwYAoFGIqx72Uc87Pd0AANRi8+bNys7Ojv5v6+UePnx49O9jjz1W/fv31xFHHKEnnnhCEydOTHo5AQBA40OjGwDgWybO2U/Nf/NmZ2dXa3TX1UEHHaRjjz1WH3/8secyAADQVMVTDxsf9XQzvBwA4FtxDS3/7ysepaWlev/999W+ffsEHREAAE1HKuvgxoSebgCAbyVqIrW6uvHGGzVixAh16tRJ27dv1y9/+UsVFxdrzJgxnssAAEBTxURqlWh0A8ABfvqJfRjwQ0d+pwFLgqbo3//+ty666CLt2LFDbdu2Vb9+/fTWW2+pc+fOqS6ar0TSAoqk1ewBiTi+1RhHmi2fM48rnFi6PTaQ8ZgWSLfHFAo60tLSHSHD0u1htWyhwVqm24MztUyzhxNzhf7KCjnCkDnCgnkNGZYVtO8vGIh9LpMTMsx+vcOOYbXljhvdNYzXdQzpluOWpFLL/lwNopKwo4yO3stwxGvjzBWqy7G/sD3NWNKMI0yXsd92ijjCgjluV+fnWtD1GeW4LWN9fkq1nEfEhUY3AMC34h2eVt+8Cxcu9LwvAAD8Jp562E8/AtDoBgD4ViTOidT8FK4EAICGFk897Kc6mEY3AMC3GrqnGwAA/A893ZX883Q6AAAAAACNDD3dAADfoqcbAIDUoae7Eo1uAIBv0egGACB1aHRXotENoNm57dO/WdN+efhxDVgSAF5E0mOH7LKFwZGksCvEl+XbUDij/nkk7+HElOEKC2YP95SWYU/LynCE8XKktcoojb3cETIsO73EmuYK79XKEU6sRdARoiwUu4yS1NKRzxU6KyMQO3ZTMkKGBR0hw1wTSJU5Ytm5GinfBDOtaXuCWdY0L8eXFbKXMRhwvAccQkH7+yPiCOPlarZFHCHDbNt05Qk4PjMCjjK6Pmsst2RlPsdnTdD1OWQ5Bj9NXNbY0OgGAPgWPd0AAKQOPd2VaHQDAHzLKL5f7r31xwAAACm+ethPdTCNbgCAb9HTDQBA6tDTXYmQYQAAAAAAJAk93QAA36KnGwCA1KGnuxKNbgCAb9HoBgAgdWh0V6LRDcCXpn+2xpp2S5cTGrAkSCUa3f5kQoGY4cFcobocUZas+bzkqcxnn/7HOEKGBdLsIZFC6fa0zHR7TKHMNHuoq5aO8F+20GCt0uxhurLT7CHDDnLkc4X3ah2yb7Nl0LVNe1qGI/xXegOGDAs5QmeFHZ89JcYRX8ohK2IPEec6vhLLG8H1+bjfFQPLwbVNV6ix8rC3axAO25+0LbeFBstwhRmzb89xihVwhCFzfQ4ZxzZdIRQjls8oY/+Y8YxGdyWe6QYAAAAAIEno6QYA+JYxAZk4fimPJy8AAM1dPPWwn+pgGt0AAN+KKBBXnO548gIA0NzFUw/7qQ5meDkAAAAAAElCTzcAwLeYSA0AgNRhIrVKNLoBAL7FM90AAKQOz3RXotENoMm6//PV1rSJnfs3YEnQWNHT7U8mVPmqsdzx0JwrzfawnXN7IUdYMEdawJEWdIUMC3lLy0izhxPLCNnjDWWFYoeXamFZXplmD/3lCgvWMuQt9Jcr7SBHmis8VkYDhgwLyn4vRAL2z56QsefzKuy42YOWOFKlIUfcPIfSiL35kRWy368VjnBcrvvcFX6t1PHesb1XI473sOvBXddt4v6s8ZjPkRaxbNO2PB70dFdq0s90z5o1S127dlVWVpYKCwv1xhtvWNddsWKFAoFAjdcHH3zQgCUGAMA/qIcBAKhdk+3pXrRokcaPH69Zs2Zp4MCBevTRRzV8+HC999576tSpkzXfhx9+qOzs7Oj/bdu2bYjiAgBSgOHlyUM9DACoDcPLKzXZnu77779fV155pa666ir16NFDM2fOVEFBgWbPnu3M165dO+Xn50dfoZB9HEVpaamKi4urvQAATYf577A2ry8/VfiJRj0MAKhNPPWwn+rgJtnoLisrU1FRkYYNG1Zt+bBhw7Rq1Spn3t69e6t9+/Y65ZRT9NprrznXnTFjhnJycqKvgoKCuMsOAGg4RpIxcbxSfQCNFPUwAKAu4qqHU134BGqSje4dO3YoHA4rLy+v2vK8vDxt27YtZp727dtrzpw5Wrx4sZ599ll169ZNp5xyil5//XXrfiZNmqTdu3dHX5s3b07ocQAA0BRRDwMAUHdN9pluSQp8a2ZHY0yNZVW6deumbt26Rf/v37+/Nm/erPvuu0/f+973YubJzMxUZmZm4goMAGhQEQUUUByzl8eRtzmgHgYAuMRTD/upDm6Sje7c3FyFQqEav6Zv3769xq/uLv369dOTTz6Z6OIBSKDHN79pTbuiYFADlgRNEROpJUeq6+FIWkCBtJrXJuKIYORKC2fUP49Jd4QMy7CHIQqm20NPpWXY0zIz7KG6Dsqwh+NqnWEPnZWdbk/LSd8fO09aiTXPIen77OUI2vO1DjnSgrHLIbnDgrUM2M9JhiP8ly00WHrAfk3LnfHo7EKOwbNhR2OjxHj7+t4yYP8BK8txvkqM5Q3ikBm036/BgLdBw0HHNfDaOKsI269dxJJWHnHsK2xPizhCnjluSUUq7Nt05nN8fgUs5Yy4js0jJlKr1CSHl2dkZKiwsFDLly+vtnz58uUaMGBAnbezfv16tW/fPtHFAwA0EvFMohZvjG8/ox4GANQFdXClJtnTLUkTJ07U6NGj1adPH/Xv319z5szRpk2bNHbsWEmVz4Ft2bJFCxYskCTNnDlTXbp00THHHKOysjI9+eSTWrx4sRYvXpzKwwAAoEmiHgYAoG6abKN71KhR2rlzp6ZNm6atW7eqZ8+eWrp0qTp37ixJ2rp1qzZt2hRdv6ysTDfeeKO2bNmiFi1a6JhjjtELL7ygM844I1WHAABIsqoZUOPJj9iohwEAtYmnHvZTHdwkh5dXGTdunD777DOVlpaqqKio2kQs8+fP14oVK6L//9///Z8++eQT7d+/X1999ZXeeOMNKnoA8LmqZ8niecGOehgA4JKKOnjWrFnq2rWrsrKyVFhYqDfeeMO67tatW3XxxRerW7duCgaDGj9+fI11HnvsMQ0ePFiHHHKIDjnkEJ166ql655136lWmJt3oBgAAAABAkhYtWqTx48fr1ltv1fr16zV48GANHz682sirA5WWlqpt27a69dZbddxxx8VcZ8WKFbrooov02muvafXq1erUqZOGDRumLVu21LlcNLoBAL5FTzcAAKnT0HXw/fffryuvvFJXXXWVevTooZkzZ6qgoECzZ8+OuX6XLl30wAMP6NJLL1VOTk7MdX7/+99r3LhxOv7449W9e3c99thjikQieuWVV+pcrib7TDcA//jd5r9a00YTFgxxiJiAAnE0nP00c6qfmGDlq8Zyx+VyRnWy5DNBR1gwx74Cjn0FHNt0hVIKOfKFgvZQSmmOMEsZwQprmi1EVqYjT1bAkeYIIZUVcKQ587n2Z0/LkCtkWOzjTnddG0foLxevIcO8CjtuzPJgyJ7Rcgu5rlvEsa9vHHGuXPdXadDebHHd5+lB+/5c76tgKPY2Xe/hiCPN1dXp+nxKRpq1LEnojo2nHq6qg4uLi6stz8zMVGZmzRB4ZWVlKioq0s0331xt+bBhw7Rq1SpPZYjlm2++UXl5uQ499NA656GnGwDgW1UTuMTzAgAA3iSiDi4oKFBOTk70NWPGjJj72rFjh8LhsPLy8qotz8vL07Zt2xJ2TDfffLMOO+wwnXrqqXXOQ083AAAAAKBR2rx5s7Kzs6P/x+rlPlAgUL1n3RhTY5lX99xzj55++mmtWLFCWVlZdc5HoxsA4FuVv5R7r2jp6QYAwLt46uGqOjg7O7tao9smNzdXoVCoRq/29u3ba/R+e3Hfffdp+vTp+stf/qJevXrVKy/DywEAvsVEagAApE5D1sEZGRkqLCzU8uXLqy1fvny5BgwYENdx3HvvvfrFL36hl156SX369Kl3fnq6AQC+Zf77iic/AADwJp562Eu+iRMnavTo0erTp4/69++vOXPmaNOmTRo7dqwkadKkSdqyZYsWLFgQzbNhwwZJ0t69e/Xll19qw4YNysjI0NFHHy2pckj57bffrqeeekpdunSJ9qS3atVKrVq1qlO5aHQDAAAAAJq8UaNGaefOnZo2bZq2bt2qnj17aunSpercubMkaevWrTVidvfu3Tv6d1FRkZ566il17txZn332mSRp1qxZKisr0/nnn18t3+TJkzVlypQ6lYtGN4AG8Yd/v2VNu6DjwAYsCZqTeIeIM7y8cTKhyles5a489U0zjm9JJs3RB2MJNSRJwTRHaKM0RyilNHsopRZpjrBaIUe+kD3fQWmlMZe3DMVeLkmtQ/vtacESb/kC9nwHBcvsaY5wYq7wX+mWt3y6I4RXuSNclYtzm7Y4XZKyjD3NFWrMGdrMcQi2kFsloQz7vhznpNzxZiyN2N905Y4YWFmOslQ48u0P2d9zpZb3cYXjPWzSHE/uhhwhCEP26+b5c81RlIgln215POKph73mGzdunMaNGxczbf78+TH24+5Tr2p8x4NGNwDAvxhfDgBA6jT0+PJGionUAABIghkzZigQCGj8+PGpLgoAAEgheroBAP4V7wzkHvOuWbNGc+bMqXdIEQAAfCWeethHj3jR0w0A8K3K+KDxvSSpuLi42qu01P5c6969e3XJJZfoscce0yGHHNJARwoAQOOTiDrYD2h0AwB8K1FxugsKCpSTkxN9zZgxw7rPa6+9Vj/4wQ906qmnNtRhAgDQKDVknO7GjOHlABLmuS1rrWlnHdavAUsCJNbmzZuVnZ0d/T8zMzPmegsXLtS6deu0Zs2ahipas2SCsWfmdc3W65rl1zZjr3HMNuyaidg1Q3nI4+zl6Y5ZljMss0tLUpZjhvIWIfvs3y0tM4PblteeZh8dclDAMQu5xxnKWwbt1ycrYL9R0i39UemOPOXO2cQdM6U7+r5cs5e70pwc90lY9vMcshzfN8Z+TV1KHPdCS8cs5K5Zz133uWv28gxHVIC0UOxmUihkL0fYcd+5Ih64PmsijpnNg4mO2EB3bNLQ6AYA+JcJxPdM2H/zZmdnV2t0x7J582Zdf/31WrZsmbKysrzvEwAAv4inHqanGwCAxi/eZ8Lqk7eoqEjbt29XYWFhdFk4HNbrr7+uhx56SKWlpc4eEgAA/CaeethPz3TT6AYA+FcDxuk+5ZRT9O6771Zbdvnll6t79+76+c9/ToMbAND8EKdbEo1uAAASonXr1urZs2e1ZQcddJDatGlTYzkAAGg+aHQDAHwr3tlP/TRzKgAADS2eethPdTCNbgCAv6VweNqKFStSt3MAABoDHw0T94pGN4B6s4UGO+uwPg1cEgDNkXUy3IbsFGngDpig41trMJD4NJuQx3BVoYDHMFcOQcc1CDX0BbJwlSMUsKdFHD189uBYtZWlcbR8nPeko4yhBN/LtbFensZxa6GJodENAPAthpcDAJA6DC+vRKMbAOBfDTh7OQAA+BZmL5dEoxsA4GsBxTcW0D+/sgMA0PDiqYf9UwcHU10AAAAAAAD8ip5uAIB/MbwcAIDUYXi5JBrdAAA/o9ENAEDq0OiWRKMbgMWLX6y3pg3vQGgwNBHW2FL1yI/GqZ4hw4zrgbqg5Zuda3uuW8OR5gpt5AqrFXDkSwva86UHw/a0gCMtWFHvPFmBMvv25CpH7H1VbtORz/GNPD1gv+CZCjnyxU4LOi5q0LGviCPEWpqjHF4fZQ27zonjGrjOsz2P/XqHHeHQMgIZ1jTbfSdJaRHX/WpPS3O8r1zvOdt71fVeDNg+SyQZV1gzj58nrs8hT59Ryajy4qmHfVQH80w3AAAAAABJQk83AMC3jKl8xZMfAAB4E0897Kc6mEY3AMC/eKYbAIDU4ZluSTS6AQB+xjPdAACkDs90S+KZbgAAAAAAkoaebgCAbwVM5Sue/AAAwJt46mE/1cE0uoFm7OUv/mZNO61D7wYsCZAkPNPtTwHFDG2T6BGM7pA73sIGOcMNOfbnCgsWdNyozjRHWWyhwVwhlkIew6Glu7bpKH+G44SlOwZzhhz5bKHB0gP2r8zlxh7mKugMT+b4Gu767HGFpHPMPJXuCF/mOs+2NNe95boXnPmcad7eA2mOcGJeQvi58rjDiVmTPH/WOD80POwvKaO5eaZbEsPLAQAAAABIGnq6AQD+xURqAACkDhOpSaLRDQDwM4aXAwCQOgwvl0SjGwDgZzS6AQBIHRrdknimGwAAAACApKGnGwDgX/R0AwCQOvR0S6LRDfjei1+st6YRFgy+x0Rq/mT5EpfoWLCu7RnXveFIc+VzRHtSxJEv4ogh5UxzbdPEHgwZtiyvTLNvz5XPVY6wIyRSmfEWhizo2J8tHJQrLFjE0TKIOMJcuRoUFbKHuSp3HHfYsdFyR1rYMfg1bLmHXPeW615w5nOmOe4hR76KiD1sm/Pes9yzrjxe39+OKIPuesiZz57k5TPPMyZSk5SA4eX79+/Xli1baiz/5z//Ge+mAQCIS8DE/2rsqIcBAI2V3+vguoqr0f3MM8/oqKOO0hlnnKFevXrp7bffjqaNHj067sIBAAA76mEAABq/uBrdv/zlL7Vu3Tr97W9/0+OPP64rrrhCTz31lCTJuMZQJMisWbPUtWtXZWVlqbCwUG+88YZz/ZUrV6qwsFBZWVk6/PDD9cgjjyS9jACAFDIJeDVi1MMAgEbNx3VwfcTV6C4vL1fbtm0lSX369NHrr7+uRx99VNOmTVPA8QxOIixatEjjx4/XrbfeqvXr12vw4MEaPny4Nm3aFHP9jRs36owzztDgwYO1fv163XLLLbruuuu0ePHipJYTAIBkoR4GAKDxi6vR3a5dO/3973+P/t+mTRstX75c77//frXlyXD//ffryiuv1FVXXaUePXpo5syZKigo0OzZs2Ou/8gjj6hTp06aOXOmevTooauuukpXXHGF7rvvvqSWEwCAZKEeBgCg8Yur0f273/1OeXl51ZZlZGTo6aef1sqVK+MqmEtZWZmKioo0bNiwasuHDRumVatWxcyzevXqGuufdtppWrt2rcrLy2PmKS0tVXFxcbUXAKDpCCjOSVxSfQC1oB4GADRmcdXDqS58AtU5ZNiePXs0depU/fnPf9aOHTuUk5Ojbt26aeDAgTrvvPPUvXv3ausPHDgw4YWtsmPHDoXD4RpfNPLy8rRt27aYebZt2xZz/YqKCu3YsUPt27evkWfGjBmaOnVq4goOJIkrLNhwwoKhOfNRyDDq4UbGT9PqNlEhx9szmOCv66GAK+SZPbxX0GP/ljufPWRYyFfNlMSwhYGrTcCSLxln2FnVuMqf5MeIEoKQYZLq0dN96aWX6plnntGYMWN011136frrr9err76qp556Ssccc4zOPvtsffHFF8ksaw3ffl7NGON8hi3W+rGWV5k0aZJ2794dfW3evDnOEgMAGpSPJlKjHqYeBoAmxyd1cLzq3NO9bNky/fWvf9Xxxx8fXXbrrbfq+eefV1pamu68806dcMIJevPNN9W1a9dklDUqNzdXoVCoxq/p27dvr/ErepX8/PyY66elpalNmzYx82RmZiozMzMxhQYAIA7UwwAANE117unOy8vTvn37YqZ16tRJjz76qK699lpdf/31CSucTUZGhgoLC7V8+fJqy5cvX64BAwbEzNO/f/8a6y9btkx9+vRRenp60soKAEghH/V0Uw8DAJocn9TB8apzo/v666/XFVdcob/97W/WdS655BK9+uqrCSlYbSZOnKjf/va3evzxx/X+++9rwoQJ2rRpk8aOHSupckjapZdeGl1/7Nix+vzzzzVx4kS9//77evzxxzV37lzdeOONDVJeAEDDi2sSNdO4HtulHgYANDV+qYPjVefh5ddff73+85//qLCwUKeeeqrOOeccRSKRas9hPf3008rNzU1KQb9t1KhR2rlzp6ZNm6atW7eqZ8+eWrp0qTp37ixJ2rp1a7VYoV27dtXSpUs1YcIEPfzww+rQoYMefPBBnXfeeQ1SXgBACsT7S3kjqvCphwEATU489XAjqoPjVedGtyRNnz5dI0eO1H333acbbrhB+/fvV8+ePdWuXTsVFxerpKRE8+fPT1JRaxo3bpzGjRsXMy1WOYYMGaJ169YluVQAACQH9TAAAE1PvRrdknTCCSdo0aJFKisr07p16/TRRx+puLhYubm5Ovnkk9WuXbtklBNo9l7+wj6k9DTCggGx+ainuwr1sP4b+LXm4kRHpXGH8XGl2W8cWxgiSQoF7WmusEdpAXsIqaDjJk4POEJdWbbpyuNKy/CYL911vhwXwZWWHgjVO80VwivdcS+Ejf3apAfsX8PLTYUjn7cwZOmOG9p1nsOWEGVe74VkpLnuc9u9LElpwfq/d1zv4YDjPeyM7uXYpvEaFsyRzdNnnlf0dEvy0OiukpGRoX79+qlfv36JLA8AAAkT7zNhjfl5MuphAEBjF0893Jjr4Pry9lMZAAAAAAColeeebgAAGj0TiG+8XFLG2gEA0EzEUw/7qA6m0Q0A8C8fPtMNAECTwTPdkmh0AwB8zM/PdAMA0NjxTHclnukGACBBZs+erV69eik7O1vZ2dnq37+/XnzxxVQXCwAApBA93UAj8uIX661phAUDPGjg4eUdO3bUXXfdpSOPPFKS9MQTT+jss8/W+vXrdcwxx8RREFRjua6J7k1xbc+49uV4DtE40sIRe1rEka/C2PtQIo64QeXGHjorYtmmK48rrcxjvnJjDxMVdoSCKreEuZKkoGObNq6wYK4yurjCgkUcHz7ljjBkzv05t2m/h2xpXu+FZKS57vOKiD1fRaT+7x3Xe9g43sOuz4ygI5/n3l5HPi+feZ6lYHj5rFmzdO+992rr1q065phjNHPmTA0ePDjmulu3btUNN9ygoqIiffzxx7ruuus0c+bMGustXrxYt99+u/71r3/piCOO0J133qmRI0fWuUz0dAMA/Mv8b2ibl1d9K/wRI0bojDPO0FFHHaWjjjpKd955p1q1aqW33norKYcHAECj1oB1sCQtWrRI48eP16233qr169dr8ODBGj58uDZt2hRz/dLSUrVt21a33nqrjjvuuJjrrF69WqNGjdLo0aP1t7/9TaNHj9YPf/hDvf3223UuF41uAIB/mQS8JBUXF1d7lZaW1rrrcDishQsXat++ferfv3+CDwwAgCYgAXVwfdx///268sorddVVV6lHjx6aOXOmCgoKNHv27Jjrd+nSRQ888IAuvfRS5eTkxFxn5syZ+v73v69Jkyape/fumjRpkk455ZSYPeI2NLoBAKhFQUGBcnJyoq8ZM2ZY13333XfVqlUrZWZmauzYsVqyZImOPvroBiwtAAD+UdcfvsvKylRUVKRhw4ZVWz5s2DCtWrXK8/5Xr15dY5unnXZavbbJM90AAP9K0DPdmzdvVnZ2dnRxZmamNUu3bt20YcMG7dq1S4sXL9aYMWO0cuVKGt4AgOYnAc90FxQUVFs8efJkTZkypcbqO3bsUDgcVl5eXrXleXl52rZtm8dCSNu2bYt7mzS6AQC+laiQYVWzkddFRkZGdCK1Pn36aM2aNXrggQf06KOPei8IAABNUCJChtXnh29JCgSqT0xnjKmxrN5liXObNLoBAEgiY0ydngEHAAA11fWH79zcXIVCoRo90Nu3b6/RU10f+fn5cW+TRjfQwP68pciaNrxDYQOWBECi3XLLLRo+fLgKCgq0Z88eLVy4UCtWrNBLL72U6qL5T6yeE2cYL1eapbfCEeMn4AoN5Ijo5Ao35Ap7FHaFNnJss9wRLinimNrHFp4p7Mxj/1pZLq/hxFz7s5/odFd4LEeoMS/DYL2GDAs5esnCjnvPFQ7NpdxxbO7zHPv6lLmutyPNlc8Wqk6SKlz3ifM+9xrCL3ZZXO83759BjjRXODHXreBlf8kIGdaAMjIyVFhYqOXLl1cL57V8+XKdffbZnrfbv39/LV++XBMmTIguW7ZsmQYMGFDnbdDoBgD4VwPH6f7Pf/6j0aNHa+vWrcrJyVGvXr300ksv6fvf/34chQAAoIlq4DjdEydO1OjRo9WnTx/1799fc+bM0aZNmzR27FhJ0qRJk7RlyxYtWLAgmmfDhg2SpL179+rLL7/Uhg0blJGREZ2L5frrr9f3vvc93X333Tr77LP1pz/9SX/5y1/05ptv1rlcNLoBAL6VqGe662ru3LnedwYAgM8k4pnu+hg1apR27typadOmaevWrerZs6eWLl2qzp07S5K2bt1aI2Z37969o38XFRXpqaeeUufOnfXZZ59JkgYMGKCFCxfqtttu0+23364jjjhCixYtUt++fetcLhrdAAAAAABfGDdunMaNGxczbf78+TWWGcfjHFXOP/98nX/++Z7LRKMbAOBvTfwZNQAAmjTqYRrdAAAfa+BnugEAwAEa+JnuxopGNwDAtxr6mW4AAPA/Df1Md2NFoxtIgj9ueceaduZhJzZgSQDAf6xf4hxf0FyhdWxpri98xhkyzBEWzEOIIkmqcIRSKgvbwyVVpNnzlYYdIZ9CsbdZGkm3lyPoCv3l2FfAEU7MEWqsxBEyLOgMq2VPi1guesTxzGfYceNFHGnprjBdjjKWeyxLuePec51nW0g3WygxV57a8pU47q9yj++PCo/5Ipb3sdf3vivMoOuzxtnw9PiZ56ce5KaCRjcAwL8YXg4AQOowvFwSjW4AgI8xvBwAgNRheHklGt0AAP+ipxsAgNShp1uSZH+QAQAAAAAAxIWebgCAf9HTDQBA6tDTLYlGN+DZH/79ljXtnMP6NWBJANjwTLc/BcKVr28LxlhWJeKavdyWL2yfbVgR+83hnL3csc1w2DHLsmOG8rKII80xQ3lpyJ72TTgj5vLMYLk9TyTTmhZyvJlcM42HXN+6neM17eWMOPaXbtlfuaMcrhnDw47iZzjOSZljhvJyeZsdf59jBvlvIrGvtySVWPLtc1xv173g2ldpxHG/OtJc93mJI831vqqwvB8jjvepHO999+eJY2Zzx+eaM81LxAbXjOce8Ux3JYaXAwAAAACQJPR0AwD8i+HlAACkDsPLJdHoBgD4GY1uAABSh0a3JBrdAAAf45luAABSh2e6K/FMNwAAAAAASUJPNwDAvxheDgBA6jC8XBKNbqBWv9v815jLL+g4sIFLAqC+GF7uT4GIJbSNl7BgcoTPceWpsIf4MY6QQpEKe1p5hSP0V5o9rdRjuKT94XRrWmbQFjKswponK2BPCzliEYVcIcNcMYxc4Y0cYznLjf3Cplv2l+74MCg33gaOljrCgoUdB1Bi7PeCyz5HqK59xhEyLBL7PnGHBXOkhe1p+y2h6mpLc93nZa5we460cMQWMsz13neF/vIYFizBn2uSPbyi463hGcPLK9HoBgD4Fz3dAACkDj3dknimGwAAAACApKGnGwDgX/R0AwCQOvR0S6LRDQDwscB/X/HkBwAA3sRTD/upDmZ4OQAAAAAASUJPNwDAvxheDgBA6jC8XBKNbkCS9OimN61powsGNWBJACQSIcP8KRCOHSrHFgZHkiKu0DqWNGeIH1ckK0c+V8iwsCPUmDOcWMgRMsyV5ggZtj8UO/xXmiPcU7orflEShIOOc+kYmJouezkzLMfgOrZyjyG8gh7DkJUbb1/fXWHB9oRbWNNKTOz7ZE8ky5rHGRbMEbpsryMs2DcV3kKGlVTY73PX+ypsea+6QgIGHO9v1+eTKwShMyxYgtOS8RYmZFglGt0AAP+ipxsAgNShp1sSz3QDAAAAAJA09HQDAPzNR7+UAwDQ5FAP0+gGAPgXz3QDAJA6PNNdqUkOL//66681evRo5eTkKCcnR6NHj9auXbuceS677DIFAoFqr379+jVMgQEAqWES8EIN1MMAgDqhDpbURHu6L774Yv373//WSy+9JEn68Y9/rNGjR+v555935jv99NM1b9686P8ZGfZZEAEAQGzUwwAA1F2Ta3S///77eumll/TWW2+pb9++kqTHHntM/fv314cffqhu3bpZ82ZmZio/P7+hiopG5oHPV1nTftKJsGCAHzG8PPEaQz0cDBsFwzUvTiCS2LA7rhA/JnZErcrtOcL/KM2eZgtRJEnlIUfIsDR7WqkjlNI3jlBKGbaQYY4TmRm0/4gScsVY8yjsGLAZcaSlB+wXL93EPj5bKDFJKvMYMsx1TsKukGFyhLly5PsmYg/j5Qr/VRKJfZ+4woJ94woL5gz9Zb8nXWHBXPd5Wdh+vlwhw6zh/RwhAR3R6Jz5nOHEHGmufO5txq7cbMvjwfDySk1uePnq1auVk5MTreglqV+/fsrJydGqVfZGlSStWLFC7dq101FHHaWrr75a27dvd65fWlqq4uLiai8AQBPC8PKEox4GANQZdbCkJtjo3rZtm9q1a1djebt27bRt2zZrvuHDh+v3v/+9Xn31Vf3qV7/SmjVrdPLJJ6u0tNSaZ8aMGdHn1XJyclRQUJCQYwAANIyqX9jjeaE66mEAQF1RB1dqNI3uKVOm1Jhg5duvtWvXSpICgZrDM4wxMZdXGTVqlH7wgx+oZ8+eGjFihF588UV99NFHeuGFF6x5Jk2apN27d0dfmzdvjv9AAQBohKiHAQBIjkbzTPdPf/pTXXjhhc51unTpor///e/6z3/+UyPtyy+/VF5eXp331759e3Xu3Fkff/yxdZ3MzExlZtqfVwEANHLxDk/z0a/staEeBgAkXDz1sI/q4EbT6M7NzVVubm6t6/Xv31+7d+/WO++8oxNPPFGS9Pbbb2v37t0aMGBAnfe3c+dObd68We3bt/dcZgBAI0eju86ohwEACUejW1IjGl5eVz169NDpp5+uq6++Wm+99ZbeeustXX311TrzzDOrzZjavXt3LVmyRJK0d+9e3XjjjVq9erU+++wzrVixQiNGjFBubq5GjhyZqkMBAKDJoR4GAKB+Gk1Pd338/ve/13XXXadhw4ZJks466yw99NBD1db58MMPtXv3bklSKBTSu+++qwULFmjXrl1q3769hg4dqkWLFql169YNXn4kz/TP1ljTru9c9x4YAP5AyLDkSHU9HAjHDqMTdITxcoXPiVjS3GHGHOHJHCHDrGGIJEVC9hsunOYIIeUIe1QStIdgSneclG8sYZ2Cjq6ndI9hwVxhrrzmCxv7NXCF/7KFE0t35Cn3HDLMcb0d5S8x3uLbu8J47Qm3cOwvdnNhryNk2P6wfV+uNNt9J7lDhpWU2+9z1/sjHHa8H23vVcf72/W54Pp8coYFc+VzvOW8hBqzRMyLCyHDKjXJRvehhx6qJ5980rmOMf+7Si1atNDLL7+c7GIBABobhpcnBfUwAKBOGF4uqYk2ugEAqIuAMQoY77V2PHkBAGju4qmH/VQHN7lnugEAAAAAaCpodAMA/Msk4FUPM2bM0AknnKDWrVurXbt2Ouecc/Thhx8m5lgAAGhqGrAObsxodAMAfKtqApd4XvWxcuVKXXvttXrrrbe0fPlyVVRUaNiwYdq3b19yDhAAgEasIevgxoxnugEA/tXAE6m99NJL1f6fN2+e2rVrp6KiIn3ve9+LoyAAADRBTKQmiUY3mqBJn/7dmnZLlxMasCQAmovi4uJq/2dmZioz0x4up0pVyKxDDz00KeVqrgJho2BFzW9jrlBdwXL79oKWiEKWSEmVafZdKZLhCClUZk8zQfsAxApbISWVBu3fTAOOrqJgoPZ7+NsirgN3KHeE9yoN2U+0KxxXiSPfNxH7sWU6boaQYsdgSk7IMHu8J1c4NNf+wo5BrK6QYd84wn+VRmKf513lLa159oftIbz2Vtj3tbfcUUZHWkm5/V4odaRVlNnPpSmPfS4DZfZzHHS8v4PlHj+fPKc53vuWMGS28ImIH8PLAQC+lajh5QUFBcrJyYm+ZsyYUeu+jTGaOHGiBg0apJ49eyb5SAEAaHwYXl6Jnm4AgH8laHj55s2blZ2dHV1cl17un/70p/r73/+uN998M44CAADQhDG8XBKNbgAAapWdnV2t0V2bn/3sZ3ruuef0+uuvq2PHjkksGQAAaOxodAMAfCve4Wn1zWuM0c9+9jMtWbJEK1asUNeuXb3vHACAJi6eepjh5QAANAUNPHv5tddeq6eeekp/+tOf1Lp1a23btk2SlJOToxYtWsRREAAAmiCGl0ui0Q0A8LmG/KV89uzZkqSTTjqp2vJ58+bpsssua7iCAADQSPipx9orGt1olK775ENr2ozDezVgSQCg7ozhm0VDCJbHDr8SK4xYFeMKJ2YJkxOxhNWR7GHGJHcYHwXt5YhYQhRJkgnZj80V9qjUFTLMY6gx6/YceSKyH3eFIwRWRcRxbJZQVpLUMlRmTUt3hM6yhQYLOsJ7RRzhvVxc23SFBSt3HLeLK2TYPkcYL1u4tz2OPCWukGEew4LtL7dv0xkWrNwRFqzCfu0Clvdj0PFZ4gpbGHB8njjTHGG8bKG/JPvnmmQPJ+YKM4b40OgGAPiXMZWvePIDAABv4qmHfVQH0+gGAPhWQ0+kBgAA/oeJ1Cp5Gw8DAEBTYBLwAgAA3qSgDp41a5a6du2qrKwsFRYW6o033nCuv3LlShUWFiorK0uHH364HnnkkRrrzJw5U926dVOLFi1UUFCgCRMmqKSkpM5lotENAAAAAGjyFi1apPHjx+vWW2/V+vXrNXjwYA0fPlybNm2Kuf7GjRt1xhlnaPDgwVq/fr1uueUWXXfddVq8eHF0nd///ve6+eabNXnyZL3//vuaO3euFi1apEmTJtW5XAwvBwD4ViBS+YonPwAA8CaeethLvvvvv19XXnmlrrrqKkmVPdQvv/yyZs+erRkzZtRY/5FHHlGnTp00c+ZMSVKPHj20du1a3XfffTrvvPMkSatXr9bAgQN18cUXS5K6dOmiiy66SO+8806dy0VPNwDAvxheDgBA6iSgDi4uLq72Ki0tjbmrsrIyFRUVadiwYdWWDxs2TKtWrYqZZ/Xq1TXWP+2007R27VqVl1eGohg0aJCKioqijexPP/1US5cu1Q9+8IM6nwZ6upEyl3642Zr24JHdGrAkAICmJFhhYoanCpU7wnE5vvHYQnyFXF0TjrRgmb0cxp6kgCPNBO07jDjyOSIYqe5PIx5QDtcBOJSF7WGbytLsF6c05EhzXNT9YXvoqcyQPc5SULG71myhxCR3eC8XZ4g1x3l27c+Vz3VO9jtCfJVZznNxuT1kmOt6u8KCfVPmKIcrLFiZPS1c5nizlrpChsU+l0F7NDo5ItU5Qwl6T3OEBHSlWcIrusIuplJBQUG1/ydPnqwpU6bUWG/Hjh0Kh8PKy8urtjwvL0/btm2Lue1t27bFXL+iokI7duxQ+/btdeGFF+rLL7/UoEGDZIxRRUWFrrnmGt188811PgYa3QAA32L2cgAAUicRs5dv3rxZ2dnZ0eWZmfYffCQp8K1fMI0xNZbVtv6By1esWKE777xTs2bNUt++ffXJJ5/o+uuvV/v27XX77bfX6VhodAMA/Is43QAApE4C4nRnZ2dXa3Tb5ObmKhQK1ejV3r59e43e7Cr5+fkx109LS1ObNm0kSbfffrtGjx4dfU782GOP1b59+/TjH/9Yt956q4KOkUhVeKYbAOBbVb+wx/MCAADeNGQdnJGRocLCQi1fvrza8uXLl2vAgAEx8/Tv37/G+suWLVOfPn2Unl75uMM333xTo2EdCoVkjIn2iteGRjcAAAAAoMmbOHGifvvb3+rxxx/X+++/rwkTJmjTpk0aO3asJGnSpEm69NJLo+uPHTtWn3/+uSZOnKj3339fjz/+uObOnasbb7wxus6IESM0e/ZsLVy4UBs3btTy5ct1++2366yzzlIoVLc5HRheDgDwr3hnIKenGwAA7+Kphz3kGzVqlHbu3Klp06Zp69at6tmzp5YuXarOnTtLkrZu3VotZnfXrl21dOlSTZgwQQ8//LA6dOigBx98MBouTJJuu+02BQIB3XbbbdqyZYvatm2rESNG6M4776xzuWh0AwB8i4nUAABInURMpFZf48aN07hx42KmzZ8/v8ayIUOGaN26ddbtpaWlafLkyZo8ebK3AolGN5Js5Ps7rGkLuhVY0wAgIZhIzZdC5UahGF0gkTL79XJEnpIJxp7V1hUJyrhCA7m+Xbnigjke+osE7Imuu9Qe6MrNts2IIz6ZM8xVuj3uUVnEfqKzHBeuJGQPL5XhCAuWVhE7LJgkpQdjn7Gg4yxH5C2MmtdtljvOl+salDjCgpWEHeG4TOx7b0+ZI2RYhSPUW4W9/CWOkGEV5fZ84TJ7mnGEDAs602whw+zn2BneyxVqLAnhxNzhyywhwxxhxjxLwERqfsAz3QAAAAAAJAk93QAA32J4OQAAqZOK4eWNEY1uAIB/MZEaAACp08ATqTVWDC8HAAAAACBJ6OkGAPgWw8sBAEgdhpdXotGNuJ38j33WtCU9chuwJADwLRFT+YonPxqdQEVEAdWcgTqY7m1W4ZBl3J8J2bfnmCTauS/XRNe2WdRr259xzGzu4prZ3DZpsHEUxJVWEbGXscwxQ3lpmn0W8hLHDOUZllnIJSkjZE8LWr7lpwXsM57bZveujdfZy13n0jV7uWuW+P0V9lnDw5b97SvLsOcJ28tYWu6YKd0xC3mk3HGeS+1pgXL7OXGlWWcvb+AZykOOGcVdacFy+z1rnb28Igl1Xjz1sI/qYBrdAAD/4pluAABSh2e6JfFMNwAAAAAASUNPNwDAtwKK85nuhJUEAIDmJ5562E91MI1uAIB/GWN/OLWu+QEAgDfx1MM+qoNpdAMAfIvZywEASB1mL6/EM90AAAAAACQJPd2okxM32MNrvNrzoAYsCQDUA7OX+1KoLKJQpGY4HJNu70twRXWyheoK2qMXObcXKrWnubjCgnl9utE4Cuq6vW2ResojjpBhjrTyCvvJLE+zf8coC9vzuUKNpTnCgrnCf4WCsdNsocQkd5guF9c2XWHBXKHZXKHGyh3nsrTCfi7DlutaWuYIM+YIGRZ2hP6KlNvLaBz5gq6QYRX2cxIqdaRZwn+5woI507yGGnPuzxEyzJlmuc8r7O8Nz5i9XBKNbgCAjwWMUSCOZ8LiyQsAQHMXTz3spzqYRjcAwL8i/33Fkx8AAHgTTz3sozqYZ7oBAAAAAEgSeroBAL7F8HIAAFKH4eWVaHQDAPyLidQAAEgdJlKTxPByAAAAAACShp5uVNN9bUbM5e8c74hXAACNlTGVr3jyo9EJlkUUjBEyLJjuCgXlCicW+zq7woIp4Aid5Qo15oou5S3ylDOjLfRXZZrjnFjCREXSHSGpHCHDwmn2a+MKL+U11FgoVP+wYJIUtHSthSz3iGQPqVUbxy3k/OgJO29MO+e5dKTZQqJVlDnyVDjK6Eorc4QFK7efsGCZPS3gzGcvii3NFcIr5DksmLfQX6FyV5rjPi+P/d4JVtjfU57FUw/7qA5ukj3dd955pwYMGKCWLVvq4IMPrlMeY4ymTJmiDh06qEWLFjrppJP0z3/+M7kFBQCkVMDE/0JN1MMAgLqgDq7UJBvdZWVluuCCC3TNNdfUOc8999yj+++/Xw899JDWrFmj/Px8ff/739eePXuSWFIAQEpV/cIezws1UA8DAOqEOlhSE210T506VRMmTNCxxx5bp/WNMZo5c6ZuvfVWnXvuuerZs6eeeOIJffPNN3rqqaeSXFoAAPyFehgAgLprko3u+tq4caO2bdumYcOGRZdlZmZqyJAhWrVqlTVfaWmpiouLq70AAE1HIBL/C/GjHgaA5ok6uFKzaHRv27ZNkpSXl1dteV5eXjQtlhkzZignJyf6KigoSGo5AQAJxvDyRoF6GACaKepgSY2o0T1lyhQFAgHna+3atXHtI/CtaSKNMTWWHWjSpEnavXt39LV58+a49g8AaGAmAa9mgnoYAJBw1MGSGlHIsJ/+9Ke68MILnet06dLF07bz8/MlVf7S3r59++jy7du31/jV/UCZmZnKzMz0tM/GrMNb2da0D/owdA8AmqOmVA8HysMKRGqGtgmmOcJ4OcIzhSxpJuStb8IEPcf+cmzUnuSa4TfgCmflGLpp62CKOMJ72cKMVeZzpJXbt+kKNVaR5ggvFbKflKDjhAUsabblkmScceDsvG7TFsKrNmFHqC5XiC/bdTXl9pBhxnG9nSG8HGmufKFSR74Ka5JCpY60ktjLgx7DgqWV2q+3K2RYqMwR+qvUkebKV9aAIcMgqRE1unNzc5Wbm5uUbXft2lX5+flavny5evfuLaly5tWVK1fq7rvvTso+AQCpFzBGgTiGp8WTt6mhHgYAJFo89bCf6uBGM7y8PjZt2qQNGzZo06ZNCofD2rBhgzZs2KC9e/dG1+nevbuWLFkiqXI42/jx4zV9+nQtWbJE//jHP3TZZZepZcuWuvjii1N1GACAZGvgZ7pff/11jRgxQh06dFAgENAf//jH5BxXilEPAwDqhGe6JTWinu76uOOOO/TEE09E/6/61fy1117TSSedJEn68MMPtXv37ug6//d//6f9+/dr3Lhx+vrrr9W3b18tW7ZMrVu3btCyAwD8a9++fTruuON0+eWX67zzzkt1cZKGehgAgLprko3u+fPna/78+c51zLd+GQkEApoyZYqmTJmSvIIBABoXI+dzq3XKXw/Dhw/X8OHD49hh00A9DACok3jqYf90dDfNRjcAAHWRqGe6vx0f2q8TbQIAkEg8012pST7TDQBAnRjF+TxZ5WYKCgqqxYueMWNGSg8LAIAmIa56ONWFTxx6un0q+8221rQv+n3ZgCUBgKZv8+bNys7+X7hFerlTK1gWVjBUMw6QcYSQkiOMly3EVyjo7RufsUdSkuQxvJTXL5+ufM6wVLYEx3m0ZpKMK5xbmj2fK0RZpMI+ZjXguHbuNFuC40R6DOHl2qYr/JrXhogrLJicoeBiLw+UOUK2uUKGVbhChlmTnOHEXKG6gh5DhtnK4gwz5gz95UhzhBMLeg0nZgkLJkmB0thpgXA8z2PBhUY3AMC/4p399L95s7OzqzW6AQBAHcRTD/toeDmNbgCAf0XktWPxf/kBAIA38dTDPqqDaXQDAHwrUROp1dXevXv1ySefRP/fuHGjNmzYoEMPPVSdOnXyXA4AAJoiJlKrRKMbAIAEWbt2rYYOHRr9f+LEiZKkMWPG1BpiCwAA+BONbgCAfyXome66Oumkk2rEpwYAoNnimW5JNLoBAH7WwI1uAABwABrdkmh0N2mRVwqsacWDNjdgSQAAaDiB/WUKhGrOzBMMOMIUub68WZJcUaICrpBOsodSCtij+Di3GXblc6RF0h1pGY40S1iniCMcWiTDERYs5AonZt+mcYT3coWIM47oWM5t2tJcl9tjWDavYcic4eNcaV7DeNlOiSOEV8CxL2dYMEd4L2e+JIQMs4XxCjn25Qr95QwZVmKfMSxUYn+Dh0rsBxfcbz9hgdLYacGw4+AQFxrdAAD/oqcbAIDUoadbEo1uAICfETIMAIDUIWSYJBrdAAAfa+iQYQAA4H8IGVbJ8cQLAAAAAACIBz3dAAD/4pluAABSh2e6JdHoBgD4WcTUMtVvHfIDAABv4qmHfVQH0+hu5Pa+dIQ1rdUp/2rAkgBAE0RPtz+Vl8UMfxRIc8SzcjxQZw015pz8x74vV0gqz1whpByTDbnDnjn2Z0kLOL45OiNgxQjxFt2VI6STcVxS4whzJVeIMldoOUuS18hfLp636XF/rjBeAcc1sIWyc4Xwct6TrhBejohVznyucGIeQ43ZyuI1LFiw1BEWrNQeFizoSAuU2U+KK02WkGGKOE6WV/R0S+KZbgAAAAAAkoaebgCAj8XZ0+21SwkAACi+etg/dTCNbgCAfzG8HACA1GF4uSQa3QAAP4sYxfVLuY8mcQEAoMHFUw/7qA7mmW4AAAAAAJKERjcAwL9MJP4XAADwJgV18KxZs9S1a1dlZWWpsLBQb7zxhnP9lStXqrCwUFlZWTr88MP1yCOP1Fhn165duvbaa9W+fXtlZWWpR48eWrp0aZ3LxPDyRmD7c92tae1O/6ABSwIAPsMz3f5UUhaz2yAQcsSXcvDUA+EKj+UKBWUJvyRJgbC9JK4QTBF7RCGFXWGiMuz5bPuLOE6xK6STK/RX0BUWzBFqzDgunNd8tlhdjSpkmOMecgk67pOAI812r7vCe9lCzkm1hPBy3EPONEdZghX2k5lWas9nCw0WKrMfnDMsmDOfK2SY/YQFShwnpcRxUkotBx5xXVSPGviZ7kWLFmn8+PGaNWuWBg4cqEcffVTDhw/Xe++9p06dOtVYf+PGjTrjjDN09dVX68knn9Rf//pXjRs3Tm3bttV5550nSSorK9P3v/99tWvXTs8884w6duyozZs3q3Xr1nUuF41uAAAAAECTd//99+vKK6/UVVddJUmaOXOmXn75Zc2ePVszZsyosf4jjzyiTp06aebMmZKkHj16aO3atbrvvvuije7HH39cX331lVatWqX09HRJUufOnetVLoaXAwD8K2LifwEAAG8SUAcXFxdXe5VaeurLyspUVFSkYcOGVVs+bNgwrVq1Kmae1atX11j/tNNO09q1a1VeXjnK4LnnnlP//v117bXXKi8vTz179tT06dMVDruGiFRHoxsA4F9Vw9rieQEAAG8SUAcXFBQoJycn+orVYy1JO3bsUDgcVl5eXrXleXl52rZtW8w827Zti7l+RUWFduzYIUn69NNP9cwzzygcDmvp0qW67bbb9Ktf/Up33nlnnU8Dw8sBAP5lFOcz3QkrCQAAzU889fB/s23evFnZ2dnRxZmZmc5sgUD1eQ+MMTWW1bb+gcsjkYjatWunOXPmKBQKqbCwUF988YXuvfde3XHHHXU6FBrdAAAAAIBGKTs7u1qj2yY3N1ehUKhGr/b27dtr9GZXyc/Pj7l+Wlqa2rRpI0lq37690tPTFTpgss4ePXpo27ZtKisrU0aGY1bK/2J4OQDAvxheDgBA6jRgHZyRkaHCwkItX7682vLly5drwIABMfP079+/xvrLli1Tnz59opOmDRw4UJ988okikf/NQP/RRx+pffv2dWpwS/R0N5jNzxxrTSs4690GLAkANCORiJyxa+qUH42NKSuLGW7JFTLMS5Ald2Qpx5dBx87CEUdYMNcmHWGiwq4wZI5b2JXPFp4p4vjm6Apd5go15gon5jnNFU7MeWG9heNqSK5r6sznMWSYbX+u0F+uMrpCy4Vc23TlK7O/eVwhw2xhwVzbDDnCggUbOCxYoNRDWDBJxpJmkhEyLJ562EMdPHHiRI0ePVp9+vRR//79NWfOHG3atEljx46VJE2aNElbtmzRggULJEljx47VQw89pIkTJ+rqq6/W6tWrNXfuXD399NPRbV5zzTX6zW9+o+uvv14/+9nP9PHHH2v69Om67rrr6lwuGt0AAP8iTjcAAKnTwHG6R40apZ07d2ratGnaunWrevbsqaVLl0ZDfG3dulWbNm2Krt+1a1ctXbpUEyZM0MMPP6wOHTrowQcfjIYLkyonclu2bJkmTJigXr166bDDDtP111+vn//853UuF41uAAAAAIAvjBs3TuPGjYuZNn/+/BrLhgwZonXr1jm32b9/f7311luey0SjGwDgX/R0AwCQOg3c091Y0egGAPhXxCiuuF8R/1T4AAA0uHjqYR/VwcxeDgAAAABAktDTDQDwLWMiMsb7DOTx5AUAoLmLpx72Ux1MozuBPn36eGva4edvaLByAAD+y5j4hqf56HkyPzGlpTKx4msFHaGzHNvzFCTK8V0w6Ao75bgf3SHDHKHGHGWJOEIwBR3hZcPpln2l1T/MmOQONeYK4eUKNeYar+nM5+FmiBWiLprF6+OqXrfpMc0ZxssVMsyyTa8hw1z5XOG9XPeXK/RXMOwIC1biCPFVbgsZ5gj9VWZPC5Q5Qn+5woLtt4f+Upk9xJfZX2JPs4UMM0kIGRZPPeyjOphGNwDAv0ycz3T7qMIHAKDBxVMP+6gO5pluAAAAAACShJ5uAIB/RSLucY618dHzZAAANLh46mEf1cE0ugEA/sXwcgAAUofh5ZJodAMAfMxEIjJx9HT7aeZUAAAaWjz1sJ/qYBrdHvzrkd4Ktsiqsfw7F61NQWkAAGheIvtLFIkx3bJzohrXrOHh2DMO25ZLUqDCPvV3wNE7E6iwf/VyzdwcKXfMXp5hTzPp9rRwhWMmcsss5ZF0RxkdM5sbx2zikZC3fK5Zz535vExl78rjtTPO6zZdM5QnY/ZySz7X/erannOGco8zm4csM41LUqDcfuChMsfs5ZZZyj3PUO5IU4ljhnJHmin1Nnt5pDR2WsQ4LgDiQqMbAOBfDC8HACB1GF4uiUY3AMDPIsZ7EF3JVxU+AAANLp562Ed1cJMMGXbnnXdqwIABatmypQ4++OA65bnssssUCASqvfr165fcggIA4EPUwwAA1F2T7OkuKyvTBRdcoP79+2vu3Ll1znf66adr3rx50f8zMuzPYwEAfMAYSfGEDPPPr+yJRD0MAKiTeOphH9XBTbLRPXXqVEnS/Pnz65UvMzNT+fn5SSgRAKAxMhEjE8fwcuOjCj+RqIcBAHURTz3spzq4STa6vVqxYoXatWungw8+WEOGDNGdd96pdu3aWdcvLS1Vaen/ZgzcvXu3pMpZU2OpYMY/APCsQpWfoQmtZE1E8fV01z/vrFmzdO+992rr1q065phjNHPmTA0ePNh7GXwkUfVwhcpjzssTdExZHXBMWW2d1dl1+cP2+9Q40iJh+wzGpsJe/kjQMQu5I804niQMO6bPjljOl+uUmIgPZi+3aUyzl7s22YCzlxuPs5dHHO8Pr7OXG9fs5RX2AzeOtGCFZfZyV1QDZ5pj9vKIY/byiGOGcuMtzTZLeaOrhwkZ1vQMHz5cF1xwgTp37qyNGzfq9ttv18knn6yioiJlZmbGzDNjxozor/kH2jLhrpjrb05oiQGgedq5c6dycnJSXQxPFi1apPHjx2vWrFkaOHCgHn30UQ0fPlzvvfeeOnXqlOripVQi6+E3tTT2TvY7CuBKAwBENeV6uLEKmEbSbz9lypSYFeuB1qxZoz59+kT/nz9/vsaPH69du3bVe39bt25V586dtXDhQp177rkx1/n2L+y7du1S586dtWnTJl/fiMXFxSooKNDmzZuVnZ2d6uIkRXM4Rql5HGdzOEapeRzn7t271alTJ3399dd1npzLpri4WDk5OTopMFJpgXTP26kw5Vphlmj37t11Ou99+/bVd7/7Xc2ePTu6rEePHjrnnHM0Y8YMz+VoCNTDjUNzeK9LzeM4m8MxSs3jOJvDMUqNrx6ubx3cmDWanu6f/vSnuvDCC53rdOnSJWH7a9++vTp37qyPP/7Yuk5mZmbMX99zcnKa/IWvi+zsbN8fZ3M4Rql5HGdzOEapeRxn0DFUtr4qTGlcw9OqhtoVFxdXWx6rfigrK1NRUZFuvvnmasuHDRumVatWeS5DQ6Eeblyaw3tdah7H2RyOUWoex9kcjlFqPPVwVR3sB42m0Z2bm6vc3NwG29/OnTu1efNmtW/fvsH2CQBoGBkZGcrPz9eb2yzDkOuhVatWKigoqLZs8uTJmjJlSrVlO3bsUDgcVl5eXrXleXl52rZtW9zlSDbqYQBAoiSqHs7Pz/dFpItG0+iuj02bNumrr77Spk2bFA6HtWHDBknSkUceqVatWkmSunfvrhkzZmjkyJHau3evpkyZovPOO0/t27fXZ599pltuuUW5ubkaOXJkCo8EAJAMWVlZ2rhxo8rK7BPJ1JUxRoFA9RmPbM8gS6qxbqz8TR31MADAJVH1cEZGhrKyshJUqtRpko3uO+64Q0888UT0/969e0uSXnvtNZ100kmSpA8//DA6y2koFNK7776rBQsWaNeuXWrfvr2GDh2qRYsWqXXr1nXeb2ZmpiZPnuz8suUHzeE4m8MxSs3jOJvDMUrN4zgTfYxZWVkNWlHn5uYqFArV6NXevn17jd7vpo56OHmawzFKzeM4m8MxSs3jOJvDMUpNvx5uzBrNRGoAADR1ffv2VWFhoWbNmhVddvTRR+vss89u9BOpAQCA5GiSPd0AADRGEydO1OjRo9WnTx/1799fc+bM0aZNmzR27NhUFw0AAKQIjW4AABJk1KhR2rlzp6ZNm6atW7eqZ8+eWrp0qTp37pzqogEAgBRheDkAAAAAAEmSuCBsAAAAAACgGhrdAAAAAAAkCY3uWtx5550aMGCAWrZsqYMPPrhOeS677DIFAoFqr379+iW3oHHycpzGGE2ZMkUdOnRQixYtdNJJJ+mf//xncgsah6+//lqjR49WTk6OcnJyNHr0aO3atcuZpylcy1mzZqlr167KyspSYWGh3njjDef6K1euVGFhobKysnT44YfrkUceaaCSelefY1yxYkWNaxYIBPTBBx80YInr5/XXX9eIESPUoUMHBQIB/fGPf6w1T1O8jvU9zqZ4LZFY1MF21MGNQ3OogyXq4Via2rWkDk4tGt21KCsr0wUXXKBrrrmmXvlOP/10bd26NfpaunRpkkqYGF6O85577tH999+vhx56SGvWrFF+fr6+//3va8+ePUksqXcXX3yxNmzYoJdeekkvvfSSNmzYoNGjR9earzFfy0WLFmn8+PG69dZbtX79eg0ePFjDhw/Xpk2bYq6/ceNGnXHGGRo8eLDWr1+vW265Rdddd50WL17cwCWvu/oeY5UPP/yw2nX7zne+00Alrr99+/bpuOOO00MPPVSn9ZvidZTqf5xVmtK1RGJRB9tRB6dec6iDJerhWJritaQOTjGDOpk3b57Jycmp07pjxowxZ599dlLLkyx1Pc5IJGLy8/PNXXfdFV1WUlJicnJyzCOPPJLEEnrz3nvvGUnmrbfeii5bvXq1kWQ++OADa77Gfi1PPPFEM3bs2GrLunfvbm6++eaY6//f//2f6d69e7VlP/nJT0y/fv2SVsZ41fcYX3vtNSPJfP311w1QusSTZJYsWeJcpylex2+ry3E29WuJxKEOro46uHFoDnWwMdTDsTTVa1mFOrjh0dOdJCtWrFC7du101FFH6eqrr9b27dtTXaSE2rhxo7Zt26Zhw4ZFl2VmZmrIkCFatWpVCksW2+rVq5WTk6O+fftGl/Xr1085OTm1lrexXsuysjIVFRVVuwaSNGzYMOsxrV69usb6p512mtauXavy8vKkldUrL8dYpXfv3mrfvr1OOeUUvfbaa8ksZoNratcxXn6+lkiOxvq5nSjUwanXHOpgiXrYpileS6/8fB0bEo3uJBg+fLh+//vf69VXX9WvfvUrrVmzRieffLJKS0tTXbSE2bZtmyQpLy+v2vK8vLxoWmOybds2tWvXrsbydu3aOcvbmK/ljh07FA6H63UNtm3bFnP9iooK7dixI2ll9crLMbZv315z5szR4sWL9eyzz6pbt2465ZRT9PrrrzdEkRtEU7uOXjWHa4nEa8yf24lCHZz6a9kc6mCJetimKV7L+moO17EhpaW6AKkwZcoUTZ061bnOmjVr1KdPH0/bHzVqVPTvnj17qk+fPurcubNeeOEFnXvuuZ626UWyj1OSAoFAtf+NMTWWJVNdj1GqWVap9vI2lmvpUt9rEGv9WMsbk/ocY7du3dStW7fo//3799fmzZt133336Xvf+15Sy9mQmuJ1rK/mci2bG+rg/6EOpg5uKp/d1MM1NdVrWVfN5To2lGbZ6P7pT3+qCy+80LlOly5dEra/9u3bq3Pnzvr4448Tts26SOZx5ufnS6r8pa99+/bR5du3b6/xy18y1fUY//73v+s///lPjbQvv/yyXuVN1bWMJTc3V6FQqMYvza5rkJ+fH3P9tLQ0tWnTJmll9crLMcbSr18/Pfnkk4kuXso0teuYSH67ls0RdfD/UAdTBzf2z27q4dia4rVMBL9dx4bULBvdubm5ys3NbbD97dy5U5s3b65WMTaEZB5n165dlZ+fr+XLl6t3796SKp/7Wblype6+++6k7DOWuh5j//79tXv3br3zzjs68cQTJUlvv/22du/erQEDBtR5f6m6lrFkZGSosLBQy5cv18iRI6PLly9frrPPPjtmnv79++v555+vtmzZsmXq06eP0tPTk1peL7wcYyzr169vFNcsUZradUwkv13L5og6OH7Uwan/DGgOdbBEPWzTFK9lIvjtOjao1Mzf1nR8/vnnZv369Wbq1KmmVatWZv369Wb9+vVmz5490XW6detmnn32WWOMMXv27DE33HCDWbVqldm4caN57bXXTP/+/c1hhx1miouLU3UYtarvcRpjzF133WVycnLMs88+a959911z0UUXmfbt2zfa4zz99NNNr169zOrVq83q1avNsccea84888xq6zS1a7lw4UKTnp5u5s6da9577z0zfvx4c9BBB5nPPvvMGGPMzTffbEaPHh1d/9NPPzUtW7Y0EyZMMO+9956ZO3euSU9PN88880yqDqFW9T3GX//612bJkiXmo48+Mv/4xz/MzTffbCSZxYsXp+oQarVnz57oe06Suf/++8369evN559/bozxx3U0pv7H2RSvJRKLOpg6uDFfy+ZQBxtDPWyMP64ldXBq0eiuxZgxY4ykGq/XXnstuo4kM2/ePGOMMd98840ZNmyYadu2rUlPTzedOnUyY8aMMZs2bUrNAdRRfY/TmMqQJZMnTzb5+fkmMzPTfO973zPvvvtuwxe+jnbu3GkuueQS07p1a9O6dWtzySWX1AiD0BSv5cMPP2w6d+5sMjIyzHe/+12zcuXKaNqYMWPMkCFDqq2/YsUK07t3b5ORkWG6dOliZs+e3cAlrr/6HOPdd99tjjjiCJOVlWUOOeQQM2jQIPPCCy+koNR1VxWW49uvMWPGGGP8cx3re5xN8VoisaiDX4uuQx3cOK9lc6iDjaEe9sO1pA5OrYAx/33qHwAAAAAAJBQhwwAAAAAASBIa3QAAAAAAJAmNbgAAAAAAkoRGNwAAAAAASUKjGwAAAACAJKHRDQAAAABAktDoBgAAAAAgSWh0AwAAAACQJDS6AQAAAABIEhrdgM888MAD6tq1q1q2bKlzzjlHu3fvTnWRAABoFqiDAcRCoxvwkVtuuUUPPfSQnnjiCb355ptav369pk6dmupiAQDge9TBAGwCxhiT6kIAiN+aNWvUr18/rVmzRt/97nclSdOnT9f8+fP10Ucfpbh0AAD4F3UwABd6ugGfuO+++3TyySdHK3tJatu2rXbs2JHCUgEA4H/UwQBcaHQDPlBaWqrnn39eI0eOrLZ8//79ysnJSVGpAADwP+pgALWh0Q34wLp167R//37dcMMNatWqVfR10003qVu3bpKkkSNH6pBDDtH555+f4tICAOAf1MEAapOW6gIAiN9HH32krKwsvfvuu9WWn3XWWRo4cKAk6brrrtMVV1yhJ554IhVFBADAl6iDAdSGnm7AB4qLi9WuXTsdeeSR0VdGRoY++OADnXfeeZKkoUOHqnXr1ikuKQAA/kIdDKA2NLoBH8jNzVVxcbEODEZw55136owzztDRRx+dwpIBAOBv1MEAasPwcsAHTj75ZJWUlOiuu+7SRRddpKeeekrPPfec3nnnnVQXDQAAX6MOBlAberoBH8jLy9P8+fM1e/ZsHX300Vq1apXefPNNFRQUpLpoAAD4GnUwgNrQ0w34xKhRozRq1KhUFwMAgGaHOhiAS8Ac+AAKAN867bTTtG7dOu3bt0+HHnqolixZohNOOCHVxQIAwPeog4HmjUY3AAAAAABJwjPdAAAAAAAkCY1uAAAAAACShEY3AAAAAABJQqMbAAAAAIAkodENAAAAAECS0OgGAAAAACBJaHQDAAAAAJAkNLoBAAAAAEgSGt0AAAAAACQJjW4AAAAAAJKERjcAAAAAAEny/wGUglcq9qIosQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1000x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA94AAAHVCAYAAAAHNSPBAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAACyLElEQVR4nOzdeZgU1dk28Lt6n51lhmEbFjVhEVEyGAHhRY3BoFFjjMEloBFMEPMqEPNGgiiQKIlbMFFQVERjVL64JDGiQlSUCFEZmMRE4hJBCAyyzj7TW53vDzI9jF3PMzM1C91w/65rLqVOn6rq6uo6Xd1Vz20ZYwyIiIiIiIiIqEN4jvQKEBERERERER3NeOJNRERERERE1IF44k1ERERERETUgXjiTURERERERNSBeOJNRERERERE1IF44k1ERERERETUgXjiTURERERERNSBeOJNRERERERE1IF44k1ERERERETUgXjiTURERERERNSBeOJNRETHnLfffhsXXXQR+vXrh2AwiMLCQowePRo//OEPE4+ZP38+LMvCvn37mp3fihUrYFkWtm3blpi2cuVKnHjiicjIyIBlWSgtLcX69esxf/58lJeXd8Cz6nivvfYarr76agwePBhZWVno06cPLrzwQpSUlCQ9trq6GjNnzkTv3r0RCoVwyimn4Omnnz4Ca01ERHTk8cSbiIiOKS+++CLGjBmDyspK3HHHHVi9ejXuvfdenH766Vi5cqWreZ533nnYsGEDevXqBQDYu3cvJk+ejOOPPx4vv/wyNmzYgC9+8YtYv349FixYkLYn3kuXLsW2bdtwww03YNWqVbj33nuxZ88ejBo1Cq+99lqTx37zm9/EY489hltvvRUvvfQSTj31VFx22WV48sknj9DaExERHTmWMcYc6ZUgIiLqLOPHj8fOnTvxr3/9Cz6fr0mbbdvweA59Jz1//nwsWLAAe/fuRX5+fquW8dZbb2Hs2LFYuXIlvv3tbyem33XXXfjRj36ErVu3YsCAAW1+Lp1tz5496NGjR5Np1dXVOOGEEzBs2DD8+c9/BgCsWrUK5513Hp588klcdtllicdOmDAB//znP7F9+3Z4vd5OXXciIqIjib94ExHRMWX//v3Iz89POukGkDjpPtxnn32Gyy67DHl5eSgsLMTVV1+NioqKJo85/FLzq666CmPHjgUATJo0CZZl4YwzzsD8+fPxox/9CAAwcOBAWJYFy7Kwdu1adX2//e1vo1+/fol/19TUYNKkSejbty/eeeed1j79Nvn8STcAZGdnY+jQodixY0di2vPPP4/s7GxccsklTR773e9+F7t27cLbb7/d4etKRESUSpI/dRARER3FRo8ejYcffhjXX389rrjiCnzpS1+C3+8XH3/xxRdj0qRJmDp1Kt577z3MmTMHALB8+XLHx8+bNw9f/vKXcd111+H222/HmWeeidzcXOTm5uLAgQP49a9/jeeeey5xWfrQoUPV9d20aRO+9KUvAQA++eQTXHTRRcjNzUVJSQkKCwuTHm+MQTweb9G2cPryobUqKiqwadMmnHXWWYlp//jHPzBkyJCk+Q8fPjzRPmbMmDYvm4iIKF3wF28iIjqm/PznP8fYsWPx61//GqNGjUJWVhZOP/10/PznP0d1dXXS46dOnYoFCxbg7LPPxqxZszB16lQ89dRTkO7UOv744xMn01/4whcwatQoDB06FH379k38cj1ixAiMGjUKo0aNQm5urriuFRUV+OSTT1BcXIzVq1fj1FNPxdixY/Haa685nnQDwBtvvAG/39+iv8OLwbl13XXXoaamBnPnzk1M279/P7p165b02IZp+/fvb/NyiYiI0gl/8SYiomNK9+7dsW7dOmzcuBGvvvoqNm7ciLVr12LOnDl48MEH8e677za5p/uCCy5o0n/48OGor6/Hnj17xJPf9rJ582YYY/CXv/wF8+fPx4UXXoj7779f7VNcXIx33323RfPv3bt3m9Zv3rx5+O1vf4tf//rXKC4ubtJmWZbYT2sjIiI6GvHEm4iIjkkjR47EyJEjAQDRaBQ//vGP8ctf/hJ33HEH7rjjjsTjunfv3qRfMBgEANTV1XX4Om7atAkA8NFHH2HMmDF46aWXsGPHDhQVFYl9srOzccopp7Ro/m251HzBggX42c9+httuuw0/+MEPmrR1797d8VftAwcOAIDjr+FERERHM15qTkRExzy/349bb70VwKH7j1NFSUkJCgoK8O677+KBBx5AJBLBvHnz1D6dcan5ggULMH/+fMyfPx8/+clPktpPOukkbNmyBbFYrMn09957DwAwbNgwV8slIiJKV/zFm4iIjillZWWJwmaH27JlC4C2X36tae2v5Zs2bcKpp56K7t27o3v37vjOd76D3/zmN5g9e3aiUNnndfSl5j/96U8xf/583HzzzYkvKz7voosuwkMPPYRnn30WkyZNSkx/7LHH0Lt3b5x22mmtXi4REVE644k3EREdU8455xz07dsX559/PgYPHgzbtlFaWoq7774b2dnZuOGGGzps2SeddBIA4N5778WVV14Jv9+PQYMGIScnJ+mxNTU1+PDDD/Gtb30rMW3hwoV4+umncdNNN2HVqlWOy8jJyUlcQt/e7r77btxyyy342te+hvPOOw9//etfm7SPGjUKADBx4kR89atfxbXXXovKykqccMIJeOqpp/Dyyy/jiSeeYIY3EREdc3jiTUREx5Sbb74Zf/jDH/DLX/4SZWVlCIfD6NWrF84++2zMmTMHQ4YM6bBln3HGGZgzZw4ee+wxPPTQQ7BtG6+//jrOOOOMpMeWlpbCtu1ElBgA9O/fH9deey3uvfdevPbaa00ivDrDCy+8AAB4+eWX8fLLLye1H17p/bnnnsPcuXNxyy234MCBAxg8eDCeeuopXHrppZ22vkRERKnCMlIeChERERERERG1GYurEREREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeBMRERERERF1IJ54ExEREREREXUgnngTERERERERdSCeeJNqxYoVsCyryV9BQQHOOOMM/OlPf3J87LZt247YerpZ9vr16zF//nyUl5d3yDo1/Pl8PvTt2xff/e53sXPnTvFxoVAIPXv2xJlnnolFixZhz549zc778L8bb7yxXZ9HWyxcuBBDhw6FbdtJbZWVlbjxxhtRVFSEUCiEL3/5y9iwYUO7r0NnLaclHnnkEfTp0wc1NTVHZPlEREREdGTwxJta5NFHH8WGDRuwfv16LFu2DF6vF+effz5eeOGFxGPOO+88bNiwAb169er09WvLstevX48FCxa0+4l3g4Ztt2bNGlxzzTV46qmnMG7cuKSTr8Mfd//99+OUU07BL37xCwwZMgR//vOf1Xkf/nf99dd3yPNorV27duGOO+7AwoUL4fE0PdTs27cPp59+Ot544w0sXrwYzz//POLxOL7+9a/j4MGD7bYOnbWclrryyiuRlZWFO+64o9OXTURERERHkCFSPProowaAeffdd5tMr62tNcFg0Fx22WVHaM0a1dTUtKn/nXfeaQCYrVu3ts8K/Ze07ebNm2cAmCeeeEJ9nDHGfPrpp6aoqMjk5OSY3bt3NzvvVPJ///d/pk+fPiYejye1nXfeeebEE09s8tq98847BoB59NFH220dOms5rXHXXXeZvLy8Nu+3RJR+Go7dDX9er9f06dPHXHXVVeY///lPp6zDrbfeajry499bb71lbr31VnPw4MF2n/fTTz9thg4dakKhkAFgNm/e7Pi4lm7nzz8uGAyawsJCc8YZZ5jbb7/dfPbZZ83O+/C/H/7wh+3+nNtiwYIFZsiQIY7jcEVFhfnhD39o+vbta4LBoDn11FPN+vXrWzzvhx9+2PTu3dtUV1e35yq3WUc+5/aSqtuOOh5/8SZXQqEQAoEA/H5/YtrnL/f+/e9/D8uy8Oqrryb1X7p0KSzLwt///nd8/PHH+O53v4svfOELyMzMRJ8+fXD++efjvffeS+o3f/58WJaFTZs24Vvf+ha6du2K448/3vFS85bMd/78+fjRj34EABg4cGDicu21a9cmHvPRRx/h8ssvR48ePRAMBjFkyBDcf//9rrfdqFGjAACffvpps4/t168f7r77blRVVeHBBx90vczPO//88zFy5Eg89NBDOPnkk5GRkYGioiLceuutjpeFt1YkEsEjjzyCyy+/POnX7tdeew0vvvgi7rnnHmRmZiamH3fccQCATz75pM3L78zlNPj2t7+Nfv36Jf5dU1ODSZMmoW/fvnjnnXcS06+44gpUVlbi6aefbtflE1H6aOmVUOmoo64i27t3LyZPnozjjz8eL7/8MjZs2IAvfvGLap9j9YozoOOvOkvFK7hS4Uq7lkjFbUedw3ekV4DSQzweRywWgzEGn332Ge68807U1NTg8ssvF/t8/etfR48ePfDoo4/iK1/5SpO2FStW4Etf+hKGDx+ON998E927d8fPf/5zFBQU4MCBA3jsscdw2mmnYfPmzRg0aFDSvL/5zW/i0ksvxfTp01FTU+N40Ny1a1ez8502bRoOHDiAX//613juuecSl6oPHToUAPD+++9jzJgxiRPgnj174pVXXsH111+Pffv24dZbb231tvz4448BAAUFBS16/Lnnnguv14s333wzqa3hdTmcz9f827qkpASVlZX45S9/iZ/85CcoLCzE8uXLsXDhQhQVFWHatGktWjfJ22+/jf379+PMM89Malu2bBkGDBiAM888s8m6V1ZWAkCTL3PaorOW02DTpk340pe+BODQSf1FF12E3NxclJSUoLCwMPG4nj17YvDgwXjxxRdx9dVXt+s6EFF6GDZsGEaOHAkAOPPMMxGPx/HTn/4Uv//973HFFVc49qmtrW3yJeKx5sMPP0Q0GsV3vvMdjB8/vkV9WrqdD38cAFx88cWYNWsWxo4di29+85v46KOPmhzHnfqkmnvvvRddunTBN7/5zaS2q666CsYYvPHGG4l9Kj8/H1/+8pfxhz/8AVdddVWz8/f5fPj+97+Pn/70p/jxj3+cEvtmRz/n9pKK2446yRH+xZ1SnHRJVTAYNEuWLHF87OGXbM+ePdtkZGSY8vLyxLT333/fADC//vWvHZcZi8VMJBIxX/jCF8ysWbOatDVcInfLLbc0u+yWzle71Pycc84xffv2NRUVFU2m/+AHPzChUMgcOHBAXF7DOv31r3810WjUVFVVmT/96U+moKCgyaXjLblsvLCw0AwZMiRp3k5/0WhUnI8xxvznP/8xAMxxxx3X5HWJRCKmZ8+e5utf/7ravyV+8YtfGABNLo83xph4PG66dOkirjsA85vf/MYYY8ySJUvMiBEjjM/nM7feemurlt/S5dTX15urrrrK9O3b1+Tk5JjTTjvNvPXWW61+vuXl5cayLLNw4ULzyiuvmG7dupkZM2aYSCTi+PgrrrjCFBYWtno5RJTepOP9iy++aACY2267zRjTONaVlJSYiy++2HTp0sX07NnTGGPMunXrzFlnnWWys7NNRkaGGT16tPnTn/7kuLw//elP5uSTTzaBQMAMGDDA3HnnnUmXml955ZWmf//+SX2lS9K3bNliLr30UtOjRw8TCARMUVGRmTx5sqmvr0/0+fzf66+/rm6X5p7TlVdemTTP8ePHi/Nr6XZubvz9f//v/xkAZsGCBc3O+/P27NljrrnmGtO3b18TCARMfn6+GTNmjFmzZo3azxhjvv71r5vi4mKzbNkyM3z4cBMKhUzfvn3NLbfc4ngJ9eeFw2HTvXt386Mf/Sip7dVXXzUAzCuvvNJk+r59+wwAM2/evGbn36CsrMxYlmUeeeSRFvdx0tbna0znPefmXHLJJaaoqCjx7+rqavPtb3/b9OnTx7z99tuJ6e217Si98FJzapHHH38c7777Lt5991289NJLuPLKK3HdddfhvvvuU/tdffXVqKurw8qVKxPTHn30UQSDwcSv5bFYDLfffjuGDh2KQCAAn8+HQCCAjz76CFu2bHGc78UXX9zsOruZ7+Hq6+vx6quv4qKLLkJmZiZisVji79xzz0V9fT3++te/NjufUaNGwe/3IycnB1//+tfRs2dPvPTSS0nfnmuMMY7TD39dGv6a+8X73XffBXDoMvu8vLzEdL/fjxNOOAH79u1r8XpJdu3aBcuykJ+f32T6Bx98gPLycvz0pz9NWu8rr7wSAPDlL38ZANCrVy8sWLAA3/jGN1q9/JYuJxaLYeDAgXjrrbdQXl6Oa6+9FhdccAFqa2tbtbzNmzfDGIO//OUvmDhxIsaPH4/7779f/FW9R48e2LNnT9LVCkR0bJKuhPrmN7+JE044Ab/73e/wwAMP4I033sBZZ52FiooKPPLII3jqqaeQk5OD888/v8k4CwCvvvoqLrzwQuTk5ODpp5/GnXfeif/3//4fHn30Udfr+be//Q2nnnoq/vrXv2LhwoV46aWXsGjRIoTDYUQiEUybNg3/+7//CwB47rnnEpdgN1wN5KQlz2nevHmJW7xuv/12bNiwAUuWLGn1+nfEFWeH/x1u8uTJ+P3vf49bbrkFq1evxsMPP4yzzz4b+/fvb3a5JSUl+Ne//oVf/vKX+NGPfoQ//vGPGDt2LBYuXIjly5c32781V501/Lm5GuzwK7jaoq3PF+i859ycz1/9NmbMGOzatQslJSWJzzdA+207SjNH+syfUpv2ze4555xjMjIyEgVUpF+dTz31VDNq1ChjzKFfnXv16mW+/e1vJ9r/93//13g8HjNnzhzz8ssvm7ffftu8++675uSTT076Rrvh2/Q9e/Y4rufhy27pfKVfvBt+Gdb+Hn/88Wa33eOPP27effdds3nzZrNr1y7xcdK359XV1cbr9ZqvfOUrLe6jmTt3rvH7/aauri6p7bjjjjOXXHJJ4t8zZswwV199tTHm0K/IF1xwgfnf//1fc/DgQePxeExlZWXisb/73e/M6aefbowx5nvf+54JBAJJ81+1apUBYFavXp3UVlxcbI4//vik6VOnTm31L95ultOga9euprS0tFXLu/vuuw0AM3DgQDN27FgTCoXM9u3bxcfPmTPHADBVVVWtWg4RpbeWXgklXd01atQo06NHjybHjlgsZoYNG2b69u1rbNtOTD/ttNNM7969mxzrKysrTbdu3Vz/4n3WWWeZLl26JI3Bh2ttwdKWPqfXX3/dADC/+93vmp1nKlxxlp2dbWbOnNmibXC49rgqrTOvOmvuCq4NGzYYAOI82usqvLY+5/a4Ao5Xv1FzeI83uTZ8+HC88sor+PDDD5t8i/d53/3udzFjxgxs2bIFn3zyCcrKyvDd73430f7EE09gypQpuP3225v027dvH7p06eI4T8uyml0/N/M9XNeuXeH1ejF58mRcd911jo8ZOHBgs/MZMmRIm+4De/HFFxGPx3HGGWe4nsfhNm7ciPz8fIRCoSbT3377bXzyySeYN29eYtqcOXMwZMgQ3HrrrbjvvvsQj8fxy1/+El6vF8cddxz+9re/YezYsYjH47jllluwdOlSAIfum4pEIqipqUFWVlZiftFoFADg9XqbLLu0tBQlJSX4xS9+0S7P0e1y/vWvf6Gurg7HH398q5ZXUlKCgoICvPvuu9i9ezeGDx+OefPmYcWKFY6PP3DgAILBILKzs1u1HCI6OjQU2Wxw0kknYenSpUlXQh1+dVdNTQ3efvttXHvttU2OHQ3j1I9//GN88MEHGDx4MGpqavDuu+9ixowZTY71Db8kP/bYY61e59raWrzxxhuYOnVqi38xbk5rnpMbLd3OGqNccTZkyJAm0w6/4uzLX/4yVqxYge7du+Pss89GcXFxi35ZbY+r0lpy1dnXvva1Jm333XcfHnvssaSrzh5//HF1WYdfwdWSGjOf115X4bX1OR9+BVzfvn3xm9/8BhdccAG2b9/e4nuwD7/6bf78+bjwwgvVYrxt3XaUfvgqk2ulpaUAmr9k67LLLsPs2bOxYsUKfPLJJ+jTpw8mTJiQaLcsC8FgsEmfF198ETt37sQJJ5zgev1aOt+Gx9TV1TV5bGZmJs4880xs3rwZw4cPRyAQcL0ubm3fvh033ngj8vLy8P3vf79d5rlx40ZUVFSgvLw88QVEPB7Hj3/8YwwYMKBJwby+fftiypQpuOCCCwAAf/nLXxIns8XFxSgtLcXYsWPx+OOPo6ioKFHwpuFD0r///W8MHz48Mb+GiuLvvfcezjrrLACHbgm4/vrrMXDgQPzgBz9ol+foZjm1tbWYPHkybr755lafEG/atAmnnnoqunfvju7du+M73/kOfvOb32D27NlNnn+DTz75JFHAj4iOPQ0nbT6fD4WFhYnCnp93+PSDBw/CGOP42N69ewNA4jLmgwcPwrZt9OzZM+mxTtNa4uDBg4jH4+jbt6+r/tI8W/qc3GjpdpbU1NRg//79OOmkk5LamvtSfeXKlfjZz36Ghx9+GPPmzUN2djYuuugi3HHHHeprsHHjRvj9flxyySVJbbt27UJxcTEA4LrrrkN9fT0eeeQR2LaNiy66CP3798evfvUr1NXVwe/3J3353JD8ctpppyWt+z/+8Q8cf/zxiUrxDbd5/eEPfxDXFTiUcmOMQX19vePYOXLkSOzdu1c8eW3p8+2M53zLLbck2q688krMmjULH330EU4++WR1GzTYtGkTgENpOGPGjMFLL72EHTt2oKioyPHxzW07OvrwxJta5B//+Efi/qX9+/fjueeew5o1a3DRRRc1+6tvly5dcNFFF2HFihUoLy/HjTfe2CTm4etf/zpWrFiBwYMHY/jw4SgpKcGdd97Z5sG9pfNtGFDvvfdeXHnllfD7/Rg0aBBycnJw7733YuzYsRg3bhyuvfZaDBgwAFVVVfj444/xwgsv4LXXXmvTOh6uYRvHYjHs2bMH69atw6OPPgqv14vnn3++XX5h2Lp1K/bv349+/frhkksuwQ9/+EPU19fjV7/6FUpKSrB27dqkLxhOOeUULFmyBOvXr28yMDSceIfDYSxYsADPPPNMoq3h1/m//vWvTU48hw0bhuLiYvzsZz9DYWEh8vLycPfdd+P999/Hq6++2urKnpZlYfz48U3i39wsJxqN4tvf/jaGDh2Kn/zkJy1eDnDog9mHH36Ib33rW4lpCxcuxNNPP42bbroJq1atavJ427bxzjvvYOrUqa16rkR09GjplVCHX93VtWtXeDwelJWVJT1u165dAJD4ta9r166wLAu7d+9Oeuznp4VCIYTD4aTHff6Xxm7dusHr9eI///lPs+vdUq15Tm4cySvO8vPzsXjxYixevBjbt2/HH//4R9x0003Ys2cPXn75ZbFfS69Kk65Ia1h2Z1111twVXD6fT30N2+MqPKD9n7ObK+B49Rs160he506pz+lepry8PHPKKaeYe+65x9TX1yc91um+rtWrVyf6f/jhh03aDh48aKZOnWp69OhhMjMzzdixY826devM+PHjxXu89+7d67iehy+7NfOdM2eO6d27t/F4PEkVWLdu3Wquvvpq06dPH+P3+01BQYEZM2aM+dnPftaibdfcfdif38aBQMD06NHDjB8/3tx+++2O99K5vce7oULr+vXrzeTJk01ubq7JyckxF154oXn//feTHv/222+bPn36mEsuucR8//vfb9L26quvmuLiYrN48WLzzW9+M6nvuHHjzLnnnps0fdu2beacc84xmZmZplu3buaKK65Q7wWU7vGuqqoyAMyll17q2K+ly4nH4+bSSy81F1xwgWNF+OaW85e//MUAMM8991yT6TfccIMBYF599dUm0xuqq5aUlAjPmIiOVi09dktj3ejRo03Pnj1NbW1tYlo8HjcnnXSS63u8Fy1aZDweT5N7Y8PhsDnhhBMc7/Hu2rVr0nod7le/+pUB4DimOGnpc3Jzj3dLx1+nx3366aemqKjI5OXlNRmH21Jj5Rvf+IYpKChQH9O9e3fj8/kS9XOMOXTP+/jx482AAQNMOBxOTJ8xY4Y5+eSTzcknn9zkHvnHH3/cADB/+9vfmsz7vffeMwDM4sWLE9Oi0agZN26cGThwoKmpqUlan+bqrHz1q181I0aMUJ+TpjXP15jOec41NTVm5MiRzX7O+7zBgwc3+dwzZcoU4/F4ktapQVu3HaUfnngTHUN+9KMfmaysLBOLxZp9bMOHjtdff93s2rXL5OTkmG3btiXaDx48aDIyMkzPnj3NP//5z6T+zzzzjPF6veY///mPq3WNRqOmrq7OXHXVVWbu3Lmmrq6uyXq/+OKLxrIs8/e//93V/BtMmzbNjB8/3rHYXHsup8F3vvMdM2bMmHaZFxGll7aeeK9du9b4/X5z2mmnmd/97nfmD3/4gznnnHOMZVnm6aefbvLY1atXG4/HY8aOHWuef/5588wzz5hTTz3VFBUVNTmh/uSTT4zf7zdnnHGGefHFF82zzz5rxo8fbwYOHJh04l1aWmqys7PNcccdZ5YtW2Zee+0189RTT5nLLrssUWyz4QT5+9//vlm/fr159913mxTi/LyWPqeOPPF+9NFHzYYNG8y6devMs88+a2bOnGny8vJMt27dzGuvvdbqeZeXl5sRI0aYO++807zwwgtm7dq15s477zShUMhcfvnlYr9PPvnEADD9+vUzZ599tnnppZfM888/b84880yTnZ1tNm7c2OTxy5YtS3yZfrjt27cbAObBBx9MWkZxcbHJz883Tz31lFm1apX5yle+Yrp37y4WFdVOvOPxuMnLyzOzZ88Wn5Omtc/XmI5/zpFIxJx33nlmypQpTb7IagAhyq66utp4PB5z8803J6Zt27bNBAIBM3HixKTHt3XbUXriiTfRMeTMM88048aNa/ZxlZWV5qSTTjIPP/xwYtq1115rpk2b1uRxJ5xwgpk8ebLjPGzbNqNGjTLXXXedq3V1yoN99NFHE+033nijueyyy1zNu8G2bdsMABMKhUxWVlbi780332zX5TT4+OOPjd/vN+vWrWuX+RFRemnribcxjZnXWVlZJiMjw4waNcq88MILjvP54x//aIYPH24CgYDp16+f+fnPf+5YrXzVqlXmlFNOMRkZGea4444z9913n5jj/f7775tLLrnEdO/ePTHfq666qskVcNpVZE5a8pw68sS7va84q6+vN9OnTzfDhw83ubm5JiMjwwwaNMjceuutjr+wNmjNVWnaFWnGdPxVZ8a0/Qqu9rwKz5i2P+e2XAHHq9+oJXjiTXSMsG3b5OXlmVmzZrXL/KqqqkzPnj3NJ598Ij7mvffeM7fddpuJx+Ptssx099prrzl+G09ERNTSq9KauyLNmI6/6syYtl/B1Z5X4RnT9ufcmVfA8eq3Y5NljJCTQESkmDVrFgAkCpsQERGRe2eddRZisRjefPNN8TFVVVU4/fTTccMNNySKdM6YMQPRaBQPPfRQ4nHGGIwZMwbFxcW47777Wr0u8+fPx4IFC5pMe/TRR3HVVVcBOJRaMmTIELz22msYO3Zsq+cPtOz5Ap3znD/99FMMGDAAoVCoSSG2l156CePGjQMA/OhHP8LOnTvx5JNPtmren9ce247SE0+8iahVSktLMX78eJx22ml4/vnnm1QPJSIiotYzxqBr1664+uqrcc8997TLPP/xj38kqqkfnibTHl5//XV89NFH+N73vueqf0c8X6Bjn3N7aeu2o/TFE28iIiIiIiKiDpSaXwW1wJtvvonzzz8fvXv3hmVZ+P3vf68+fu3atbAsK+nvX//6V+esMBERtYv6+npUVla26a++vv5IP41jCsdsIqJjD8frpnxHegXcqqmpwcknn4zvfve7uPjii1vc74MPPkBubm7i3wUFBR2xekRE1AHq6+sxsH82du+Jt2k+PXv2xNatWxEKhdppzUjDMZuI6NjC8TpZ2p54T5w4ERMnTmx1vx49eqBLly7tv0JERNThIpEIdu+JY2tJf+TmuLtoq7LKxsDiTxGJRI6KgTwdcMwmIjq2cLxOlrYn3m6NGDEC9fX1GDp0KG6++WaceeaZ4mPD4TDC4XDi37Zt48CBA+jevTssy+qM1SUiSnvGGFRVVaF3797tVuwmK/vQnxtxVjZJGxyziYg6V3uP2RyvGx0zJ969evXCsmXLUFxcjHA4jN/85jf4yle+grVr1+J//ud/HPssWrQoKUqBiIjc2bFjB/r27XukV4PSAMdsIqIji2N2+zsqqppbloXnn38e3/jGN1rV7/zzz4dlWfjjH//o2P75b88rKirQr18/jMW58MGfvB6+5GkNPBlBsc3KzXFuCMp9jF/+zsRkOK+Hp0ouThDrpkRCeZx/KYh0CYhd4oHW/7rgicm7YjRT/sbNE5X72X5hPZTV05YVy3Se7lXqPsQy5DZvxHm6rXwlZtlymycmt0WEbxsz98rbL5wnbyhv2Hl6XN5t4VFu8wlUOq+Hti003rDz/KTpAOCvlVcwmukV27xh5xfFVy/Pz6O0icupVnY05Vtpa+9B54aQ/B629x2Q56csK15TlzQtZqL4C/6E8vJy5OXliX1borKyEnl5edj9Qb82XbrWc9B2VFRUNLl/mDpHqozZngznyxYt5XJGSxmXERTeTwH5s4GtvAdNwHn/tgPyscj2K23C/ADA9jkf68UxVOmj9TPy6sFW2oy3nefn5tChfG4wSpvl4lO2q/m5/DSvfqaQhin1c4i8ItL8LGU41D7jScty0wcAPBHnJ+YNyytoRZVxPix/KBP7hYUPhs20mbDzhzKjFCaz653n115jNsfrZMfML95ORo0ahSeeeEJsDwaDCDoMsj744bMcTrwdpjXwWPLganmEgdyrnHh7lRNvr3Di7VWOyj7lvgnhxNv2K89JGazlxcjrZ/zKibcy2rg58dY+nBjppVIGIakPAEifCyy3J97KcU3anbwBeft5lS9QxN1J3i3UE2+f33mGcfltpfLZwom3MB0AfD55BY3ygdZrCyfeMWVAVpYlLkd7D2sn3h7hRZGOPQBs7ZhlKcuyhA8aBu16ua8NW/vs12xfSj/tPWZL47L4fmmmTXw/CWMyANhe5cTb53zMsYXpzbcpJ97CWNneJ97ql8rtfOKtzk87B5Ce1tF64q2d9Lo58fa0/sRb+9FA+4wnfW5U+2htwljujSsn3rYyznujre8nfOY+1CY3GWG7G+VDo63tnO04ZnO8bnRMn3hv3rwZvXr1OtKrQURErRQ3BnGXF2y57UdHFsdsIqL0w/G6UdqeeFdXV+Pjjz9O/Hvr1q0oLS1Ft27d0K9fP8yZMwc7d+7E448/DgBYvHgxBgwYgBNPPBGRSARPPPEEnn32WTz77LNH6ikQEREdEzhmExHRsS5tT7w3btzYpLrp7NmzAQBXXnklVqxYgbKyMmzfvj3RHolEcOONN2Lnzp3IyMjAiSeeiBdffBHnnntup687ERG1jQ0D2+W1lW77kXscs4mIjk0crxsdFcXVOktDkYCzApc43+OdoVXRUu6J7JHv3BCR7w2xuyp1+YV7VExA/p4l3E25EdnFHhJTCpRJtHvJpPu7ACCS3fp7UNT7wpT7naTCYdr8tHuUjfCSSLfJAvr9Yr5aF8tSnm9Uqbnnk+p1aLcMKdvJl1yTC4C+LTQeIYNCK66mbdtAlXyfkRUV2pT7o7xKcTVvnfN731JyNTyVwgYE5OOPUFilWRGlwEtVddK0mIng1arftktxlIbj8NZ/9UKOy2ItVVU2Bg4uO2qKtZCzxJgd/DZ8DvdzW1JxNWE6ALXoqVSsUBt7baEYKiAXUdPqkMSVeii2UrPDFvrFlVva1fu/hWO9Ps4ryxLatD7afdyu2rSPGlqbm0/Z2vyk4aYD7vGWbg9Wa83IH13FfmrBM2V+0j3j2jivLksolCoVUAUAj1ZcTSuwGnH+cGMJ0wEAdUqBVeGcwSh9pIJsMRPBa3Ur2zxGcrxOlra/eBMR0bGL36ATERGlPo7Xjdqeik5EREREREREIv7iTUREaYdVUomIiFIfx+tG/MWbiIjSjt3Gv9ZasmQJBg4ciFAohOLiYqxbt058bFlZGS6//HIMGjQIHo8HM2fOdHxceXk5rrvuOvTq1QuhUAhDhgzBqlWrXKwdERFRaurs8TqV8cSbiIjSThymTX+tsXLlSsycORNz587F5s2bMW7cOEycOLFJFe7DhcNhFBQUYO7cuTj55JMdHxOJRPDVr34V27ZtwzPPPIMPPvgADz30EPr06dPqbUFERJSqOnO8TnW81JyIiEhxzz33YOrUqZg2bRqAQxnTr7zyCpYuXYpFixYlPX7AgAG49957AQDLly93nOfy5ctx4MABrF+/Hn7/ocrW/fv376BnQEREREcaT7xdsDJCsJyiSUJKzIgWNSawu8hZTrZfy8NybqsvkNdPj4Zw/rYp3EVeBy2eQoo0iWbK+RkxZfNpURO2EIUiRZMAgK3Ef0lxXdr6aXEnHuckB9fqCuU2r7AsN/FpgBIzoiRhSK8HAMQynaf7auQ+Gk/UeX/S9nU9YkZ+IX11zsvyV8kbN9JF3tE8mc7L8lcpO7uRI5CMx/mJeZS4M6tWiSfzaTu1w7K0DetS3Bz6c9sXOBR1crhgMIjg5+KiIpEISkpKcNNNNzWZPmHCBKxfv97dCgD44x//iNGjR+O6667DH/7wBxQUFODyyy/Hj3/8Y3i9yvalVhPH7EzhwK2M5SYoH8RMyPkjlRYnFs9Q2oTYMDuoxYkpEV9KnJjUTxsP1Tgx4Wlp89MOE67ixFy2SVFe7X4Y045fLuLJOiROTGhr7zgxK6ZEb2rzEz5vaJ/xPMpnFK8QvWl8yvqFlYg8j9LmE8ZlJT5X3QWFcUMN3BXWz7I9gPIRoLXaY7w+WvBScyIiSjvtcc9YUVER8vLyEn9Ov17v27cP8XgchYVNv9UqLCzE7t27Xa//J598gmeeeQbxeByrVq3CzTffjLvvvhu33Xab63kSERGlGt7j3Yi/eBMRUdqxYSGuf5ev9gWAHTt2IDc3NzH98792H8763NUBxpikaa1aB9tGjx49sGzZMni9XhQXF2PXrl248847ccstt7ieLxERUSppj/H6aMETbyIiOibl5uY2OfF2kp+fD6/Xm/Tr9p49e5J+BW+NXr16we/3N7msfMiQIdi9ezcikQgCAeW+DCIiIko7vNSciIjSjm3a9tdSgUAAxcXFWLNmTZPpa9aswZgxY1yv/+mnn46PP/4Ytt14Id2HH36IXr168aSbiIiOGp01XqcDnngTEVHaif/30jW3f60xe/ZsPPzww1i+fDm2bNmCWbNmYfv27Zg+fToAYM6cOZgyZUqTPqWlpSgtLUV1dTX27t2L0tJSvP/++4n2a6+9Fvv378cNN9yADz/8EC+++CJuv/12XHfddW3fOERERCmiM8frVMdLzYmIKO20ZUBubb9JkyZh//79WLhwIcrKyjBs2DCsWrUqEf9VVlaWlOk9YsSIxP+XlJTgySefRP/+/bFt2zYAhwq7rV69GrNmzcLw4cPRp08f3HDDDfjxj3/s6jkRERGlos4cr1MdT7xdsAIBWB6HSwFzc+ROQkQBANhB53wNKWoAAGwhZgQAYlnOL6tHiYyIZirLyhViRpS4hpgSDSZFcmjxFFpbVE5dE+Or3EZK1ecL81O2rRppImwmLXJFi+rQ1l2KPPNXyX3ickKVOD9vRO6jvsZCxIf2nLT4FOm1Dwv7MwD4a+QZRrK0KB7nlQznyiufcUDeaaSYHu2YEO0qv1hW1HnDe2qUPDu/lvsjbycrKzkXzrJ9QIU8u3QwY8YMzJgxw7FtxYoVSdOMso0ajB49Gn/961/bumrUDHHMFi7pdxMZBshjuR2UB4FYSG6T4r+kmDGtz6F+YpPLODG5TRr31Pkpn0il+anjqxYP6WJchkd+T4t9oIxTrjop/Vxekqt9NnQTJ6ZtW3F+LqPfpGgwLcZLixODVDBTez2Ul1F7icVlabQYN6khLr/A0hpY9tF1sptKeOJNRERpxzYWbPVTjd6XiIiIOh7H60Y88SYiorTDS9eIiIhSH8frRjzxJiKitBOHB3GX9UGVKyuJiIioHXG8bsSq5kREREREREQdiL94ExFR2jFtuGfMHGX3jBEREaUqjteNeOLths8HeFq36YxXqfItVDyN5cglSK2YUmFRqOYYC8kXOMSD8vrFQs5tHmUdPBG5TVqWViU93FVuk6phH2p0nhxVCtDHA/K6eyPCuivVYmNZchlKb71QtTYkr4OvRqlo61OqrgrbN5qrvY6tr04fz5TnFyiX190I2zCiVMH11sttUvXcgFLFPaJUPNeO/VIV8lC5vC3qu8g7fKDaeZ+JZsvHHSuu7LfC9Fi+HAngicgXeHlq5dL1llM1b6USq1u8Z4xaLBQAPMGkySYjeRrQTOXykHxAkqqXx5Wq5nEX43JcrVwut2njlHS8jLutai5sQjeV0AH584FxMeYBcFehXKtercxPmqHjsbK5ddD6uaxqbsflhbmpaq59bpD6aZ/jtKQUW+jn1falWOs/16gV8j1yo1epri5VXtf6qITVUC9ttoTWdh6zOV434ok3ERGlnbjxIK59GlL7tvPKEBERkSOO1414jzcRERERERFRB+Iv3kRElHZsWLBdfndsu70mk4iIiFqF43UjnngTEVHa4T1jREREqY/jdSOeeBMRUdpp2z1jR9c36ERERKmK43UjnngTEVHaOXTpmrtvwt32IyIiotbheN2IJ94u2PldYHuTY0ismJyHYEJyjofxOn8LZGsRZCE5KyGcJ0SaaLFMSvyXFJUUyZbXz6NEEUgxGVrMSDRbbvMoURPS+1WLLvMoURPRXOGJKV/I2VlyLJNlt/4tGMmX9zNLWXc3jK1E0wSFbaG89nEtzibovBF9tUp0Tkien/TlakSJkvPILxX81XKbJbz+Mee0ov92kptsn3NjOE/+xjirTN4vpGOJpRxjtFKiVlTZUJbDPJ2mEXWWYBBwGLOl2DA72PrIMACICeOyHVQiw4S4TkCOBosp8Z9uIsMA+fOB2/nJcWLKZw1tOPQ699PGcqlPc21iNJgW8aVFjblI/9LmZ0tjrMu8Y/VzgxA1psWJaTFuUjyZJ6p83tU+r0WFPsqPq0r6l0x5QbTNrq2HV4ry0lZD3eGFPtpYLjUcbaXEUwhPvImIKO3Y8CDOYi1EREQpjeN1I554ExFR2uE9Y0RERKmP43UjnngTEVHaseFhPAkREVGK43jdyN1WICIiIiIiIqIW4S/eRESUduLGQtxlMSG3/YiIiKh1OF434ok3ERGlnXgbirXEj7JL14iIiFIVx+tGPPF2wTIGlsPN/naWnB0Uz5RzN1xFkAgRX4ASHaD0iWUo0WBCXINHSTWIZcptYp8spVF538WylVgQITLEUmKypD6Ay5gRn5y7EReixiwlWsNS1s+qk/cZI8W4KLEgdkjLDJGbJLE8JYZK2LYRJW7HV6UcyJXXWFwFZfW0SDspIiWorIMnKm/AcK7z8/LXKX26yG9Ib9i5nzciv76xHCUC0S9vd29VffLjOyCaxDYe2C6LtdhHWbEW0pmAD8ab/HHHBKQ4Mfm9FA/I+5w0ZkuxYIAeDSb10yK+tNhQNRpMaFMjyJT5GZ8Q/xVo/XgNABBeEqOMr9pYKY03AOBxM84r89NiOcX5SRmVAIzwC6Cb5QBQPxsaKWpMWVZcyeuSYsjUyLCIsn7SorRN0e432bbvL7KWMq7FbWWfFsY1Kyaf6nmEPkb7gO8Cx+tGvMebiIiIiIiIqAPxF28iIko7vHSNiIgo9XG8bsQTbyIiSjs23BddUW6gICIionbE8boRT7yJiCjttC0XlHdZERERdQaO142OrmdDRERERERElGL4i7cL8Qw/LF9yOU+nSueJPkolVHidL7+IZsl9tIrI0Szn+cWU6tDxkNgkVo30huU+agVoYdXjIfk52UHlHg+luqadKVQNjyuXvISU0tZCN60CqSrgvCxPpnxxjR1XKpfnyf28QedlGWVbWNpu63OeX7hc3pk8WtX1HGG71ynVNZXXPibML7hfqVgsBxOI1VgBwBdxnh7OlfsEy5VKrcKR2SjvOamyOgAY4RgTyZNLFgf3KwvT3o6h5GOjHW//i8XixoO4yyqpbvtRejIBr2NVczsgJIq4qFwOyFXI4y4qlx/qJ6yDVtXcReVyQK5erlUhV+cnVDVHQDuQalXNnds8Xnl+HqWqudZPqlDuUcZ5V1XIxR76smxpftqlvMrC4spnCjvm3KZVUFer0wufN7RK6FrFc0tI3YGlrZ88P1dXQ6t9XFS0V94ilq1UjJeK8WuV0AV2XPlA4QLH60Y88SYiorRjw4LtMsbFbT8iIiJqHY7XjXjiTUREaYffoBMREaU+jteNjq5nQ0RERERERJRi+Is3ERGlnbblgvI7ZyIios7A8bpR2j6bN998E+effz569+4Ny7Lw+9//vtk+b7zxBoqLixEKhXDcccfhgQce6PgVJSKidmcbq01/1Lk4ZhMRHZs4XjdK2xPvmpoanHzyybjvvvta9PitW7fi3HPPxbhx47B582b85Cc/wfXXX49nn322g9eUiIjam/3fb9Dd/B1tuaDpgGM2EdGxieN1o7S91HzixImYOHFiix//wAMPoF+/fli8eDEAYMiQIdi4cSPuuusuXHzxxa1ath3wwPa1bkcwHhdxIko8WTRTidDyC3ENSvSHFkUkRY1Fc+Q+WhHCaK5zVoL2pZaW1iVFhgGAJcRa+HKE/CcA8YicNeEPxZyXI8SPAEC0Xn6b+TOc56dGdSgbSlo/AAgFnHM3ojH5+dZVyflaUhxLRrc6sY/2zWW0znk7GcjrFy2QskQAK+z8Ho1lya+Vr0ZZP6Wf9J7zVYtdEO4mt3nrhXXIUN4kQowgAAQqnV8rb0TZb7PlqDFPXO4XOJC88lrUIh0bjuiY7ffC9iUfR+JB52NLXI0MU9qE2DBt7NUiDKWIL7WP66gx5/eoFidm/Fqb8zHHEqYDgMfX+jav0sfrkdt8WgyZMJ5r8/MoeV1SVWZtLPcqmVJSsSltfNUOwbG4PMbGhKgxLdY05pHnJ8WXahFkdkSJ0JI+W2vJalEXEV9uhzC1n/N6aMvS4sSkZVnKZzxpNzNKH2qbo+trBMWGDRswYcKEJtPOOeccbNy4EdGo84f3cDiMysrKJn9ERHTk2cbTpj9KbRyziYiODkdivF6yZAkGDhyIUCiE4uJirFu3TnxsWVkZLr/8cgwaNAgejwczZ85U5/3000/Dsix84xvfaPV6HTOfPnbv3o3CwsIm0woLCxGLxbBv3z7HPosWLUJeXl7ir6ioqDNWlYiImhGH1aY/Sm0cs4mIjg6dPV6vXLkSM2fOxNy5c7F582aMGzcOEydOxPbt2x0fHw6HUVBQgLlz5+Lkk09W5/3pp5/ixhtvxLhx41q9XsAxdOINAJbV9MUz/7325vPTG8yZMwcVFRWJvx07dnT4OhIRUfP4i/fRj2M2EVH66+zx+p577sHUqVMxbdo0DBkyBIsXL0ZRURGWLl3q+PgBAwbg3nvvxZQpU5CXlyfONx6P44orrsCCBQtw3HHHtXq9gDS+x7u1evbsid27dzeZtmfPHvh8PnTv3t2xTzAYRDCo3ExFRERE7Y5jNhERNfj8rUPS8T4SiaCkpAQ33XRTk+kTJkzA+vXr27QOCxcuREFBAaZOnapeuq45Zr72Hz16NNasWdNk2urVqzFy5Ej4/XIRISIiSj1xtOXyNUp1HLOJiI4O7TFeFxUVNbmVaNGiRY7L2rdvH+LxuOOtSp//Mrc13nrrLTzyyCN46KGHXM8DSONfvKurq/Hxxx8n/r1161aUlpaiW7du6NevH+bMmYOdO3fi8ccfBwBMnz4d9913H2bPno1rrrkGGzZswCOPPIKnnnrqSD0FIiJyqS2XjPNS887HMZuI6NjUHuP1jh07kJubm5je3NVNTrcqSbcpNaeqqgrf+c538NBDDyE/P9/VPBqk7Yn3xo0bceaZZyb+PXv2bADAlVdeiRUrVqCsrKzJTfQDBw7EqlWrMGvWLNx///3o3bs3fvWrX7U6lgQA4LEO/X1OLMNd+X3b67wjSBFFAOCVU5QQyRUalH0+miG3GWEv0eK/YplKzIiU/pAfFvvYUWXbyqkb8AScf9vyKNEVvkx548aFCI28DDlCK5Aj/75WH3PeuLlBIU8KwK5y+f4TLSKlV65zhd+9Ndlin7xMeT2kda+tlzNrLDeZHCElEkZ7rWLO6xHPVHYYZWCQ3gcAAGHXjSvvKykyDJDfI+J7G0BAKeAsRRZq0UiWT36tPFXyPh3LTt7usZiyzV2KG48Yq9OSvtS5juSYbQed48Tk6E0l/lOIDAOAmNCmRXyp8V/C50rXcWLB1keDmYDy3g22Pv7LJ4zJAOBVxi+/z7mfNB0AAl65zae1CRlL2vjlU6LGYloElMCjLEuKDXN7XIsIYzkARISosbgSeVrvla9IkWLIYkqMq1HiWo1XiDuzlLFc/aje+hMz7bOwK8oMlZQ5sZ8Va/1+Efe2b5xYe4zXubm5TU68Jfn5+fB6vY63Kn3+V/CW+ve//41t27bh/PPPT0yz7UMvhs/nwwcffIDjjz++RfNK2xPvM844I1FoxcmKFSuSpo0fPx6bNm3qwLUiIiKiz+OYTUREHS0QCKC4uBhr1qzBRRddlJi+Zs0aXHjhha7mOXjwYLz33ntNpt18882oqqrCvffe26oEjbQ98SYiomOXgQXbZSyYYZwYERFRp+js8Xr27NmYPHkyRo4cidGjR2PZsmXYvn07pk+fDgBJtzYBQGlpKYBDt0Xt3bsXpaWlCAQCGDp0KEKhEIYNG9ZkGV26dAGApOnN4Yk3ERGlHV5qTkRElPo6e7yeNGkS9u/fj4ULF6KsrAzDhg3DqlWr0L9/fwBIurUJAEaMGJH4/5KSEjz55JPo378/tm3b5mq9JTzxJiKitGMbS7zXsSV9iYiIqOMdifF6xowZmDFjhmOb061N2q1QLZ1HS/BrfyIiIiIiIqIOxF+83bDNob/PiWbJVQBjmfI3Np6oUE1U+ZKnvqvcGM1xnq5VQtWu5LADzusXz2h95XIAQI5zJWqjVLUMZEXEtmAgJrZFY87z9CgVSLOCyrL8zsvaX5Ul9unbtVxs83ucK6tqFVK7ZdeKbUGvvC2kSq1dM+T5aZVVs4TKvwVZ1WIfrYK6tMtYlvx6SFXmASAuVEM3EblPrIu8/Tx18v4Z6ea8LG+dvCxvWH6ThLs7Tw/tE7uI73sA8B5wnq5VaPbVyq99NEd5r1Ym9+uIe6rj8CDu8rtjt/0oPcUDHli+5Nc8HnLeD/TK5fJypIri2tgbDyltLuZnK5XLbaVCuRHGeUurQh5UKoP7ndukMRRwV6E85JOTLbSq5iFtrBTGXw+0qubysqQYJe2XPG1+Mdv5+BtzeSlvfVw+FZDSS6LCOgB6uor0mSzildchqrTFhYQapeg6rKg2Hknb0N0Y5ibIRZ2fi6rmHuVzkrR+tqd9x0iO14144k1ERGmHl5oTERGlPo7XjXjiTUREaceGB7bLb8Ld9iMiIqLW4Xjd6Oh6NkREREREREQphifeRESUduLGatNfay1ZsgQDBw5EKBRCcXEx1q1bJz62rKwMl19+OQYNGgSPx4OZM2eq83766adhWRa+8Y1vtHq9iIiIUllnj9epjCfeRESUdhruGXP71xorV67EzJkzMXfuXGzevBnjxo3DxIkTk3JAG4TDYRQUFGDu3Lk4+eST1Xl/+umnuPHGGzFu3LhWrRMREVE66MzxOtXxxJuIiNKOMR7YLv9MK6v/3nPPPZg6dSqmTZuGIUOGYPHixSgqKsLSpUsdHz9gwADce++9mDJlCvLy8sT5xuNxXHHFFViwYAGOO+64Vq0TERFROujM8TrVsbiaC7FsP+D3Jzdo8QVyMgSimc47lScm5xDEMuT5SV8OaeugkfZ5Ky4/YTtbjuqwpGgDIRYCADweuS07FBbbquudc1e02BItCiNuO6+7FhlWFZbzYvrnHnScXhtz2L/+K+pVYuuUA5TUpsWqqPMTtoW0jQDgpPwyse3ve3uJbeI6eORtYWU77xfRsHzYs+vlNi3Gw+Q6709WpfJaKe9hW1gNbfzxyKlrCOc5v1d99XKfuF9eWKhc3hjeuuRtYWIuDz4drLKyssm/g8EggsGmx4xIJIKSkhLcdNNNTaZPmDAB69evb9PyFy5ciIKCAkydOlW9dJ3axvg8MA77s+11fl/YPmVs09qEw7b0fm6uzUjHAb8S5elT8ouUfpYQNeZVIsikyDBAjg0LKXFiIb8cDSZFZWrjl9YWcBG9KcV/AnrUmO0iisrN/LSILzW6TBncpDa30WVeF/laag/L+Tlrlycb5TdHExfiyeSPZOpnYUvpB2GzK2myzRybWjcdACy/cAzsgAhQOuTo+hqBiIiOCXFYbfoDgKKiIuTl5SX+Fi1alLScffv2IR6Po7CwsMn0wsJC7N692/X6v/XWW3jkkUfw0EMPuZ4HERFRqmuP8fpowV+8iYgo7djGfb6n/d8fNXbs2IHc3NzE9M//2n04y2q6LGNM0rSWqqqqwne+8x089NBDyM/PdzUPIiKidNAe4/XRgifeRESUdhru/3LbFwByc3ObnHg7yc/Ph9frTfp1e8+ePUm/grfUv//9b2zbtg3nn39+4zrZh64v9Pl8+OCDD3D88ce7mjcREVEqaY/x+mhxdD0bIiKidhQIBFBcXIw1a9Y0mb5mzRqMGTPG1TwHDx6M9957D6WlpYm/Cy64AGeeeSZKS0tRVFTUHqtOREREKYS/eBMRUdqxYbkuANPafrNnz8bkyZMxcuRIjB49GsuWLcP27dsxffp0AMCcOXOwc+dOPP7444k+paWlAIDq6mrs3bsXpaWlCAQCGDp0KEKhEIYNG9ZkGV26dAGApOlERETprDPH61THE28iIko7cWOplWub69sakyZNwv79+7Fw4UKUlZVh2LBhWLVqFfr37w8AKCsrS8r0HjFiROL/S0pK8OSTT6J///7Ytm2bq3UmIiJKR505Xqc6nni3J6UAgJagEBfSpqJKbIBHTt1ALNN5uhaHEMtWVlBoMkr8l6XElniECBI7LEdhBJQIEi2+qkdOleP0cFze9aXYEgAIeJ3XPaDEjPTPdo4MA+TIkKJMuc9n9TliW3lEzqjqk1nuOD3DK+9Me8LysiLCNgwp89sXzhLbhhU4V4jeUd1F7KO99nsrsx2nhzLk3K2IEiUX8yqHyxrnNi3aJ9JD3s+C/3F+s8bkzQdvndwmRQla8iro8WnKTUp2wCG2ydP+dzV19j1jM2bMwIwZMxzbVqxYkTTNmNZVhHGaB7WPuN9yjM2JB53H2HhAiewJaMtpfR91fkEh2iigRE2F5DeuFZDHKW9QGNsCynFKacsQosGyA3L8p5tosEyffDzP8MptQY+8LL+Q5+RTMln9SlvUyJ9tJF4pawpAXLhLNKYsRzt5qZN2XAB1cecdNKJEl2lRaBGfcz+/V34jaHGyYeHDtZKuibgQQQYA0mFbHTO0Q7120ij0iytjrxYLHLedl6V8PIUl9GnvX5l5j3ejo+vZEBEREREREaUY/uJNRERpx4blPp7kKLtnjIiIKFVxvG7EE28iIko7pg3FWsxRNpATERGlKo7XjXjiTUREacc2bfgG/Sgr1kJERJSqOF434j3eRERERERERB2Iv3gTEVHaYZVUIiKi1MfxuhFPvF2I5Hhg+5N3BC2CRN1vhEgBLTKsvkCZnbAasazWxds0sDOdswi0qCRfUI7qsKPOG6OgsKJ1K/ZfWUo8iRQbpkWGZfrkDZ/td17WCVl75XWw5bfZ3ohz5FV1TInWULLp8kPVYptfyIcqj8oRZD4lUyon6Lws7fl2CciZVzEhnkS7zEiLE8vOcH6tqmqE/D7osSUZOfJ+VidFcsSVSMBKeTuJxwst9U85mkspM1rEoFHiDH11SjRNfvK+G4sq+Sgu8dI1ainbZ8F22J+lQ5X2XlIOb2I/7X1mK9GbRmiTpgOA5Zffax6lzSfEfGpRnlJkGABk+p0DnbTxVYsGk2Iqs5XIMLdxYiHhw5dHGQ/bP05Mfo3jwj2vUWXn1O6v1dZd+tygjfPaiVK98JnM7Tgvr4MW46UsSxizjTKWG2H8BwCjRHbawu6k7Jrq8ccjHX+U3c/puAi0/xjJ8boRT7yJiCjt2G0o1nK0VUklIiJKVRyvGx1dv98TERERERERpRj+4k1ERGmHl64RERGlPo7XjXjiTUREaYcDORERUerjeN2IJ95ERJR2OJATERGlPo7XjXji7YLxWDAehwqpSuVApRgm4kIB67hcbBreWrktmiOthNwHSqVsCBVU/VlyxVC/UCEVAIxfqsgpb8CQTy7z2DOzSmyrFaqDa29krTJ4rq/ecbpWtVSrnvrFrM8cp1fEMsU+XfxyZfBegXKxbUtNL8fp4/I+Evt8FssV26QKqgeVdd8dl8v7dheqpGuVZPfUOVeFB4AM4TUuyJJf3/+UdxHb4nG5JEZGnvN+UWvLb2JPjbzPxIXC607HnQY+5ZggbcKIdKwAEDoot8WDSrX2WPLxwrR/UXOiFrP9zpXFpYq+ymFKrSosjeVaH1cVzwNa5XJ57PUF5LZQwLmSd6YwHQCylUSRbKGqea7f+VgJ6FXIs4WK5xkeuU+mV16/TKWfVOU7YMljeXtXNfcoVc2lYlMRpRy/9pmn1hMU26o8zoORm+cEACGv8zpqaS0ar8f5vWArlca1j8JSEok2Py29xJIDamAJ85SOIwCg7ILiccujHWOk53uUFTRLJTzxJiKitMNv0ImIiFIfx+tGPPEmIqK0Y+D+W3l3v60QERFRa3G8bsQTbyIiSjv8Bp2IiCj1cbxuxBxvIiIiIiIiog7EX7yJiCjt8Bt0IiKi1MfxuhFPvImIKO1wICciIkp9HK8b8cS7HWmRYbFMZceRLvhXKgpoyQuR7s6xFp6oEoegJEMEcp0jOSxlJQJ+OfMgGnNeWK+cSrHPwTo5okqLocj2y3EiEikyDACyhXiSfsH9Yp+yaBexzSu8yNr8am0la0IxJKvMcXpFXN62tpHvRpHW4wsZzhFpzYkJO+EJWXvFPtprv6vGOQqtol6O+MoMyBEz1fVy5Ep9rfO2yOgi70t1RsgMAwBLeEMqhxETUd7fQlNITuKDFZe3rRZ3YrwOUYtW+w+cHMippYzXcowOk6K8lFQmNf5L6qf3kd9nRogTs3zyhw2vX24LKuNy0Of8uSFTiAUD5MgwAMj2OY+V2viaJfQB5PivHK88v0yPNj+5LSBEg/k7MU7Mq4xtceH4VW/cfTYI2XJknPS86l1Gl9Vpg4eL+UmfAaJxd3FnUmxoVIkMQ0AZe235M5S0y1jKsrRjkxHmJ8UmHmpz3n7tHQHK8boR7/EmIiIiIiIi6kD8xZuIiNKOMRaMy2/C3fYjIiKi1uF43Ygn3kRElHZsWK5zQd32IyIiotbheN2IJ95ERJR2eM8YERFR6uN43Yj3eBMRERERERF1IP7iTUREaYf3jBEREaU+jteN0vrEe8mSJbjzzjtRVlaGE088EYsXL8a4ceMcH7t27VqceeaZSdO3bNmCwYMHt8v6RLOUCADt2gIhNSKaI3fRoss8YeeF2Vly3IXxKNEVMef5hUJyBIX2RskIyv0k3TNqxLY8f53YFvQ4x39I0STNyfdXO07fF5NfrKiS1ZYpxKcElNiSMORsGi3SRGJD3pkGBivEtgOxLMfpWtyZFpGSF3Detvsj2WKf2pi8rB7CPlPulbfR3hp5WdrlTpnZzq9jzUE5usxSjglGeK+aqHzIjmYp8X4VzuuuRZOE85T38AElAsnheanHP5d46Vr6OVJjtvEe+kuaLuyX6v6qvW+l+XmV94vSZgltHi1OzOuuLeBzHnMCyvEy5JXH8gyhLcMrj73auJwpRHm6jQzLUtqkcVQbl9s7Tsyj5MlK8Yxeo+TMuhQXdmqPkjcV9ir5eVIfWx6MQl55u8eEuC5pfwbkODYACAvvEem9CAC20qYeL4TdQjv+aLuSm+OZ9PFUixh2g+N1o7Q98V65ciVmzpyJJUuW4PTTT8eDDz6IiRMn4v3330e/fv3Efh988AFycxvzfQsKCjpjdYmIqB3xG/T0wjGbiOjYxPG6Udre433PPfdg6tSpmDZtGoYMGYLFixejqKgIS5cuVfv16NEDPXv2TPx5ve38tQ4RERE1wTGbiIiOdWl54h2JRFBSUoIJEyY0mT5hwgSsX79e7TtixAj06tULX/nKV/D666+rjw2Hw6isrGzyR0RER57576Vrbv6Otm/QUx3HbCKiYxfH60ZpeeK9b98+xONxFBYWNpleWFiI3bt3O/bp1asXli1bhmeffRbPPfccBg0ahK985St48803xeUsWrQIeXl5ib+ioqJ2fR5EROSOAWCMy78jvfLHGI7ZRETHLo7XjdL2Hm8AsD5XYMIYkzStwaBBgzBo0KDEv0ePHo0dO3bgrrvuwv/8z/849pkzZw5mz56d+HdlZSUHciKiFGDDggWXxVpc9qO24ZhNRHTs4XjdKC1PvPPz8+H1epO+Kd+zZ0/SN+qaUaNG4YknnhDbg8EggsFgi+enVQjWrpSIZTpP98nFuhHuqlRYzBCqMmbKVR4Rl1cwHnG+p86fXS/2iUTl+/AKc6ocp2f65AqpWvVUN8JGrrrZM1AutuV4nV8UaToAxH3yhSVfCDr/2vOX6kGO0wHgzOz3xbb3w33EtlNC2x2n/yvSS+zjV6q4FvqdK57/vVYulNTVJ1enl6rC/jsqVwYvDMmXktbEnN+7vTPlSu2fVcvV6btmya9xVKisWp8h72fS+woATNi5zQ7JlWQ9EXk/iwjHC8uW3/e+WrEJsYzWDYRx4eSKjg1Hesy2fRYsX/I+aAtvT2k6AMTlIAWxn/ErVc0Dynva73xM9AXkCtrBgDxWZgXkquE5Aecq37l+ufq3liiS63P+fNDVL48BOR75M0WO17ktxyOvg1a5PNOSt0VAGIu0yuV+JWom6iLWwav8zhcXTkTqtQ+hikxL/pwbErZTvVHeCIqgx3n/9CiJJxqPsN3dnqzF4kIqkDAdAKLKOKp9traFzw1aOI0dk+cn9dOOZ5awfrb2nKhN0vJS80AggOLiYqxZs6bJ9DVr1mDMmDEtns/mzZvRq5d80kFERKmpoUqq2z/qPByziYiOXRyvG6XlL94AMHv2bEyePBkjR47E6NGjsWzZMmzfvh3Tp08HcOiSs507d+Lxxx8HACxevBgDBgzAiSeeiEgkgieeeALPPvssnn322SP5NIiIyAXbWLCYC5o2OGYTER2bOF43StsT70mTJmH//v1YuHAhysrKMGzYMKxatQr9+/cHAJSVlWH79sZLayORCG688Ubs3LkTGRkZOPHEE/Hiiy/i3HPPPVJPgYiIXGoovOK2L3UujtlERMcmjteN0vJS8wYzZszAtm3bEA6HUVJS0qTgyooVK7B27drEv//v//4PH3/8Merq6nDgwAGsW7eOAzgREVEn4ZhNRESdYcmSJRg4cCBCoRCKi4uxbt068bFlZWW4/PLLMWjQIHg8HsycOTPpMQ899BDGjRuHrl27omvXrjj77LPxzjvvtHq90vrEm4iIjk28Z4yIiCj1dfZ4vXLlSsycORNz587F5s2bMW7cOEycOLHJVVWHC4fDKCgowNy5c3HyySc7Pmbt2rW47LLL8Prrr2PDhg3o168fJkyYgJ07d7Zq3XjiTUREaYcn3kRERKmvs8fre+65B1OnTsW0adMwZMgQLF68GEVFRVi6dKnj4wcMGIB7770XU6ZMQV5enuNjfvvb32LGjBk45ZRTMHjwYDz00EOwbRuvvvpqq9Ytbe/xPpLCeRZigeQdQUi7ONSnq9wmlvpX9jUluQLwON8QYWrllzvQVV75jJBznITXI69EQIkvyBViS6qjcjxF14CcbSTFRgFAbsj5eY3O/ljsUxkPiW2fxZzfkCFLjnAp8DnHpwFAvRBr1j+4T+yzI9ZdbBscLBPbJB7Ir2MPr7zuUqTJkIxdYp+t4QKxLVt4A2mxIFoESa+Qc2zYZ+FcsU9RbrnYVhGR9wufMDBUKOtnovL3nt5M5/3J2iWvgx2UlxUod16WlnIjxRwCetSh07FJi0dxi8VaqKWMx3lfl3YDNf1J2XWMNPZqY7myLEuYn3bc8wp9DrXJx3qf8KEi4JEjJbUIraDQL6REVIaEqKlD/Zzb9D7asuS2AKQ4Mfn5+rXXRIkGc9NHGnvdiis7YdQjxF4qn0G1z0O2sKxaZZCQ9iUACHucP9dK+zMA+D3ysqT3j8crz096nwKArbRJP31qxx83berxTGpr559l22O8rqxsGh8rxUdGIhGUlJTgpptuajJ9woQJWL9+vat1cFJbW4toNIpu3bq1qh9/8SYiIiIiIqKUVFRUhLy8vMTfokWLHB+3b98+xONxFBYWNpleWFiI3bt3t9v63HTTTejTpw/OPvvsVvXjL95ERJR2WCWViIgo9bXHeL1jxw7k5jZesej0a/fhLKvpL+zGmKRpbt1xxx146qmnsHbtWoRC8pWITnjiTUREaefQQO5uEOWJNxERUedoj/E6Nze3yYm3JD8/H16vN+nX7T179iT9Cu7GXXfdhdtvvx1//vOfMXz48Fb356XmRESUdlhcjYiIKPV15ngdCARQXFyMNWvWNJm+Zs0ajBkzpk3P484778RPf/pTvPzyyxg5cqSrefAXbyIiIiIiIkp7s2fPxuTJkzFy5EiMHj0ay5Ytw/bt2zF9+nQAwJw5c7Bz5048/vjjiT6lpaUAgOrqauzduxelpaUIBAIYOnQogEOXl8+bNw9PPvkkBgwYkPhFPTs7G9nZ2S1eN554ExFR2jH//XPbl4iIiDpeZ4/XkyZNwv79+7Fw4UKUlZVh2LBhWLVqFfr37w8AKCsrS8r0HjFiROL/S0pK8OSTT6J///7Ytm0bAGDJkiWIRCL41re+1aTfrbfeivnz57d43Xji7YI3AjgFLESVLzw8zolch+YnXPBvy+laapyY8Qq7qS1frqFdylEXdl6R3l2c45oAwFKiNQpDlY7Ta5WYrG7+GrGtLi5vqDyfcwzZP+r6in2+GJIjuU4K7RDbJDujctRAF6/z8zorc6vYZ0csQ2yLGvktLUWXDQ/uFPv8M9JbWZZzzIgWTzYkJC8rLtz5MixH7rM/miO27Y04vyG1aBItpqcgQ94Ht1d0cZyeEZJjVWL18mslpbvEusgxKIG98vxsockrbwoIL+9/G+WmaFbytHgHjDRtuWScl5ofW4zXeX+W9nFt31fbhP3c+JQ3jBJT5PE5t/l9SvSST35TZ/iU6C3hYJDhlftk+ZyjQQEg0+vcluOVswhzPHKsqdQvx5L7ZCkfvLKUqDEpGsyvHDb8SsRXVM1/dTE/YYwNGXk5WgSZGncmzFKL5Kr3yp/JvMK2kD5PAEBYGsAARIWsrJCyDjElX6vO6/y8wsr7NCa8TwHA+JQ7eoXP6sarfFZ3cWzS4sRsKS1OG/9dOBLj9YwZMzBjxgzHthUrVjgsRz/FbzgBbyueeBMRUfrhT95ERESpj+N1AourERERNWPJkiUYOHAgQqEQiouLsW7dOvGxZWVluPzyyzFo0CB4PB7MnDkz6TEPPfQQxo0bh65du6Jr1644++yz8c4773TgMyAiIqIjiSfeRESUftpSIbWVl66tXLkSM2fOxNy5c7F582aMGzcOEydOTLpHrEE4HEZBQQHmzp2Lk08+2fExa9euxWWXXYbXX38dGzZsQL9+/TBhwgTs3CnfWkFERJR2OnG8TnU88SYiorRzKBfU/V9r3HPPPZg6dSqmTZuGIUOGYPHixSgqKsLSpUsdHz9gwADce++9mDJlCvLy8hwf89vf/hYzZszAKaecgsGDB+Ohhx6Cbdt49dVXW7spiIiIUlZnjtepjvd4ExFR2mmPYi2VlU0LPQaDQQSDwSbTIpEISkpKcNNNNzWZPmHCBKxfv97V8p3U1tYiGo2iWze5GCMREVG6YTHURjzxdiGaCdjB5OnalzJaVUGpLZolzzGeI1dRtIRKib5sucKn5ZGX1S3buTJ4VcRhI/zXsO67xba99c6VqLsE5Gqn2UKFVADI88n9wrZzJe8vhuT16+GtEtv2xJ3XvY/voNhnQGCv2JbjcX5eB5Qy0L2VqrCfxuQq3yHLuTqtVu1Ue15S9fK/1feT5+eX5/defZHjdK3iaoZStfbE7HLH6TvDXcU+HqvlWYyH65Lh/JrsqAuJfbrlV4ttFVXOleuVouuIZ8nHBF916y9u0o5ZEecfcQEAGXuTVzIeSc2vrIuKmu5zTrEg+/btQzweR2FhYZPphYWFiRzP9nDTTTehT58+OPvss9ttnnSI8Tjvz9I+rlUO1qr9ioki0nTIlcsBwOuiqrlfqMoMAAGlEnVIqF6e4ZWPsZnK8Vdq0/vI43yW5dzPbeXyTOUzT0iIlfArF4n6pSgKAFGl2rjE46KquTS9+YXJ+0UcztvXqzynWiO/jpJ65bXPVCqUS9XQpf0Z0KuaB4RUAJ9X/kzm9coHhbiyn0lpB+JxBICtVDz3tGNKgzb+U9vwxJuIiNJPW+79+m+/HTt2IDc3NzH58792H86ymi7LGJM0za077rgDTz31FNauXYtQSP6yhoiIKO20w3h9tOCJNxERpZ223PvV0C83N7fJibeT/Px8eL3epF+39+zZk/QruBt33XUXbr/9dvz5z3/G8OHD2zw/IiKiVNIe4/XRghcTEBFR+jFt/GuhQCCA4uJirFmzpsn0NWvWYMyYMW16CnfeeSd++tOf4uWXX8bIkSPbNC8iIqKU1EnjdTrgL95ERESK2bNnY/LkyRg5ciRGjx6NZcuWYfv27Zg+fToAYM6cOdi5cycef/zxRJ/S0lIAQHV1Nfbu3YvS0lIEAgEMHToUwKHLy+fNm4cnn3wSAwYMSPyinp2djexsd7UGiIiIKHXxxJuIiNJOZ1ZJnTRpEvbv34+FCxeirKwMw4YNw6pVq9C/f38AQFlZWVKm94gRIxL/X1JSgieffBL9+/fHtm3bAABLlixBJBLBt771rSb9nAq8ERERpStWNW/EE28iIkpPnXgJ2owZMzBjxgzHthUrViRNM83cmNZwAk5ERHTUO8ouGXeLJ94ueKOAU0X/uFwQFxGlfk9cSErw1cnf8sRzlXgSv3M0RCwsv9yZOfViW1W98xPrmVvpOL052X7nZXXxyzFZtbYcJ1EXd44MA+QYsvJ4ptgnxyOvhxQ1liVEdQHA3rj84vvh/FpFlWiS/TF53ffH5UtUj/fLsWaSHI+8X+yIOecNj8v8SOyzR1m/4wJ7HKdvqe8j9slUYuak2LCwrbwPfHI0TUzJEaqLOe+DXq8SuVIv79NiFU9bPiZYMblNespKMgksOWEGSoIfbH/yTO0O+Maa36BTS4kFdTtrN+jE3c2jfLr1KHmEUpvWR+N1EW3ltVzGYQk8ynb3duaL4oJXSUyQjqfyp5BmlpUCZ0Tqvqmsn7ed91uJGmCR2rtSSuB43YjF1YiIiIiIiIg6EH/xJiKi9NOWaqdH/gceIiKiYwPH6wSeeBMRURqy4P4av6Pr0jUiIqLUxfG6AU+8iYgo/fAbdCIiotTH8TqB93gTERERERERdSD+4k1EROmH36ATERGlPo7XCTzxdsETdY6piIXkPr5aZX5CglFUTl6C8cl7otkv5JrlyWETti1f/JCfW+04PRyXd5/KqLIxBEFPTGzLlDYSAL9HjiDJ9Dr36+krF/tkeeSIqo8ihY7TvxT6VOzzBSXGS4rxqDdydJVfiVzpokShSf12xeS4swKv82sPAAN8+x2n77fluLNaI2fu7Y7mOU7PVF4PLTIkFHTen/5y8ASxT7/MA2Lb+xU9xTa/xzl7q3t2jdinvDZDbAvXOceTGZ/82sfl2cFX7fz+dor+aqC85dRjnVM8Ylx+Cd0TM6Ja2JeOLa2IEzPatYAe5VOgND+XUUTS8U2L3bKUY6JPGSulY5hfyRX0K2O21C9kKWO5EK95aH7Oywpp66d8YvcrkZ1BOI+/fkselz3KC+kRlmUrkWs+YR0AuLrlNa5tC2W7a9tX7iO/xnEhlytgyfGa2n7ms4X9VtifAcCnvH+k95b2WUN7z1nK8cJI/VweL6TjjKvjT3sPkRyvE3jiTUREaceYQ39u+xIREVHH43jdiPd4ExEREREREXUg/uJNRETph/eMERERpT6O1wk88SYiovTDe8aIiIhSH8frBJ54ExFR2rHMoT+3fYmIiKjjcbxuxHu8iYiIiIiIiDoQf/F2IRYCjEPyge2cAAQAiMspShCTo5QYAm+V/NLZuc7RC76QHMkQ8MttsbjzChZmVYl9tOiF7gHniKUufjkKK9tXL7YN9u8S20Ie5wi1uPKdU8iSY9cGBcqEPnJ0xUfRArGttxBrVm/Lr28fnxxRVaPEkOW4iAUpt+WMqj5e59d/f1zOwauIy1FjBb5Kx+m7ol3FPl4ljuVALMtxet+Mg2KffWElw08REaL16qLyQaE+LLd5/c6vlYkr35XWy5dj2WJSixI9VCvPzygjh78ieZqSLuMe7xmjlrLgGI/j5gpGrY/Y5jJuSIopEhKZAOiRYR5lx5fatLFcixqTYpm8yvy0mDQpDlOK5ASAgLKh/MpnAK/QT4sM81vyQTFqnD9feZTIMG1+4lPWoumU0tB+ZRyVtq+23bX9THr91T5qmxD/pY1tStSYmwg/91FjztP1+C8tzlDoqHxscBVB5gbH6wSeeBMRUfrhPWNERESpj+N1Ak+8iYgo/fAbdCIiotTH8TqB93gTERERERERdSD+4k1EROmH36ATERGlPo7XCTzxJiKi9MOBnIiIKPVxvE7gibcLxuNciTwgF/lGWC5eiZhQcdgOyntbPFuuyujPci4hbJQCBbV1YtljZAWd52cr8/usVq4OLfWLGvnOB21ZUaUCeN/AAcfpWoXKf4V7i22jMrY694n0EPuMCX0mtlUIqxHyylXmM5VKrR7I+0Vfn3OV7wN2tdhHq2peL1RQPz3kXPkdAP5aXyi2Ffmdq43X2EokgEKqaP+vup5in/JISGzrmSG/wSNC5f8D1XIV92BAfo1rqp2fs4kqr728S8Nb59xPK3TvCcttcXkzwemtpbzd3GOxFmop4UOfm3xYtaiw0KaNvdq+KPVTClSrY6WtlL2W2tT5KWN2XGiLK/OT+mjrEVfGw4hpfZV0APAIy9KqV0uVywHAFs4cbKWauHayERPG+ajyfOPKDKNKm5QAE3exLwHy66/2Uduc10+bX8yWP5CL+5nLz6fae196HytBB83EKrRyOuRjVrtnZ3O8TmjzPd51dXXYuXNn0vR//vOfbZ01ERERtSOO2UREREdGm068n3nmGXzxi1/Eueeei+HDh+Ptt99OtE2ePLnNK0dEROTEMm37OxZxzCYios7G8bpRm068f/azn2HTpk3429/+huXLl+Pqq6/Gk08+CQAw2rVQ7WTJkiUYOHAgQqEQiouLsW7dOvXxb7zxBoqLixEKhXDcccfhgQce6PB1JCKiDmDa+HcM4phNRESdjuN1QptOvKPRKAoKCgAAI0eOxJtvvokHH3wQCxcuhKXcd9MeVq5ciZkzZ2Lu3LnYvHkzxo0bh4kTJ2L79u2Oj9+6dSvOPfdcjBs3Dps3b8ZPfvITXH/99Xj22Wc7dD2JiIhSAcdsIiKiI6dNJ949evTA3//+98S/u3fvjjVr1mDLli1NpneEe+65B1OnTsW0adMwZMgQLF68GEVFRVi6dKnj4x944AH069cPixcvxpAhQzBt2jRcffXVuOuuuzp0PYmIiFIBx2wiIqIjp00n3r/5zW9QWNi0SnEgEMBTTz2FN954o00rpolEIigpKcGECROaTJ8wYQLWr1/v2GfDhg1Jjz/nnHOwceNGRKPO1Y/D4TAqKyub/BER0ZFnoQ33jB3plT9COGYTEVFn43jdqMVxYlVVVViwYAH+9Kc/Yd++fcjLy8OgQYNw+umn4+KLL8bgwYObPP70009v95VtsG/fPsTj8aQPEIWFhdi9e7djn927dzs+PhaLYd++fejVq1dSn0WLFmHBggVJ0331gNchtSHqnNZ0iLbnCAkQnrDcyYrJL10s7tzPlyfnA+Vm14ttNWHnqLFYXP7epme2HL1UEHSOrwp65DiOrv4asS1kyf38QlvUyNvvpNB/xDavcLPJAP9+sc+nMTkOq8DrvN17eeRtuzkiR1QN8svRYB9G6xynh5R9s6dXnp9kXV0fsa23zzkyDADeq+/rOL3WlqPuCnzyfnYw5vyGrIzKr8ewLnIU2vsVcgxZTcR5nlpkWH3YL7Z5/c4HBbtaOyYokStCNGGgUukjJ8nB67wrHernEDUmHJLahvEkKo7ZKeRoqw6UJrzK29zTzh/nvZYWN+Uc/+Vx+duX3E+OE/Medacv7mmxcBJL6dPeW1YdntQ8wxR+jTleJ7T4XT9lyhQ888wzuPLKK/Hzn/8cN9xwA1577TU8+eSTOPHEE3HhhRdi165dHbmuST5/T5oxRr1PzenxTtMbzJkzBxUVFYm/HTt2tHGNiYioXbBYi4pjNsdsIqKUwPE6ocW/eK9evRpvvfUWTjnllMS0uXPn4oUXXoDP58Ntt92GU089FX/5y18wcODAjljXhPz8fHi93qRvyvfs2ZP0DXmDnj17Oj7e5/Ohe/fujn2CwSCCQfnXMSIiolTEMZuIiCi1tPgX78LCQtTUOF/u269fPzz44IO47rrrcMMNN7TbykkCgQCKi4uxZs2aJtPXrFmDMWPGOPYZPXp00uNXr16NkSNHwu+XL/kkIqIUxG/QVRyziYgoJXC8TmjxifcNN9yAq6++Gn/729/Ex1xxxRV47bXX2mXFmjN79mw8/PDDWL58ObZs2YJZs2Zh+/btmD59OoBDl5xNmTIl8fjp06fj008/xezZs7FlyxYsX74cjzzyCG688cZOWV8iImo/rgu1mGPjlluO2URElAo4Xjdq8aXmN9xwAz777DMUFxfj7LPPxje+8Q3Ytt3kXqunnnoK+fn5HbKinzdp0iTs378fCxcuRFlZGYYNG4ZVq1ahf//+AICysrIm+aADBw7EqlWrMGvWLNx///3o3bs3fvWrX+Hiiy/ulPUlIqJ21JZvwo+ygdwJx2wiIkoJHK8TWnziDQC33347LrroItx111344Q9/iLq6OgwbNgw9evRAZWUl6uvrsWLFig5a1WQzZszAjBkzHNuc1mP8+PHYtGlTB68VERHRkccxm4iIKHW06sQbAE499VSsXLkSkUgEmzZtwocffojKykrk5+fjrLPOQo8ePTpiPVOL8M2NdjmE7ZXb4iHnjvEsORoCXmVhAed+Ho/cx+eRl5UddI4h81pynx2VXcS2TJ9zBmvXgBwZtjucJ7Z9KftTsU2KDevilZe1I9pVbOvirXWcXqDMr7dXjpTKtJzvVfzMlvt08chZTjke+d7HT2POd5acGpT7vBeRl1WvRLJJPorIkVwDAnsdp2+qGyD2+TjsXJgJALr6nF+ToXnO8UUA4FXexF0CcuRezHbetlLMGABUVsp5XXbU+YBhZcn7Berkg4yn3rkKtHZcUtJxoCS8AQ5vb205rvEb9BbhmI3/hsgmT3aTUqP1EdtcxgNJEUZeZSzXopJ8ypjtEd4Ufss5CuvQsuT5Sf20+QWUNnl+8vPVIrS0Nr/lfMCSpgN6NJhfWFTcaNtPHl+jxnkc8GsHbYVf2aml7RtXosu019jNfuGmTdqfAX2/lT4La/NTo8aU96oY6KDMz7iJDHNxzGr3BC+O1wmt/+T8X4FAAKNGjcKoUaPac32IiIia1ZZ7v462e8ZagmM2EREdCRyvG7k+8SYiIjpijOX+a/l2/zqfiIiIHHG8TnB3XQoRERERERERtQh/8SYiovTDe8aIiIhSH8frBJ54ExFR2uE9Y0RERKmP43Ujnni7EA8CcChWrBReVKsKesPOjT6lSnG4QFlYjXO/mF+eX3mNXGE56Heuep2bIVd5Pr7rfrGte7BabJP0CZaLbTW2XDl6e7i74/T/yfmX2MerVOsMWc4V2WttuTL4LiO/Vt08zvOrUubXRegDABW2vKOV210cp2+PHVT65IhtRb4qx+key7k6OQAciGeKbX44b6cCYTkAUBUPiW1/ry5ynB625cNe0CNXDa+Nya9JbdS5zHdceT0CQXlZ9ZXO87Ol8rgArAx5P/PVOD9nbUBTNgW8zkEHh+bpsBpCEd624Tfo1FIukkgkWh+pzWjLUe5fNEKbdlyxlfnFjHx3oS18SIka+XODrcxP6qfNL6K0yfOTj3txpXp1VBnnPco8JcqhWV1HuY980LSFA1hUqZKuLks5IEaF11iafqjNzevY+j5am7Q/A0BMidmQEkq0+UnvUwAwyntVOi54lD6uTkJdHLPa/WT3CIzXS5YswZ133omysjKceOKJWLx4McaNG+f42LKyMvzwhz9ESUkJPvroI1x//fVYvHhx0uOeffZZzJs3D//+979x/PHH47bbbsNFF13UqvXiPd5ERERERESU9lauXImZM2di7ty52Lx5M8aNG4eJEydi+/btjo8Ph8MoKCjA3LlzcfLJJzs+ZsOGDZg0aRImT56Mv/3tb5g8eTK+/e1v4+23327VuvHEm4iI0o9pvHyttX/8xZuIiKiTdPJ4fc8992Dq1KmYNm0ahgwZgsWLF6OoqAhLly51fPyAAQNw7733YsqUKcjLy3N8zOLFi/HVr34Vc+bMweDBgzFnzhx85StfcfxlXMMTbyIiSj+mjX9ERETU8dphvK6srGzyFw473/MWiURQUlKCCRMmNJk+YcIErF+/3vVT2LBhQ9I8zznnnFbPkyfeRESUfnjiTURElPraYbwuKipCXl5e4m/RokWOi9q3bx/i8TgKCwubTC8sLMTu3btdP4Xdu3e3yzxZXI2IiIiIiIhS0o4dO5Cbm5v4dzAoF1YGAMtqWqTOGJM0rbXaY5488SYiorTDeBIiIqLU1x7jdW5ubpMTb0l+fj68Xm/SL9F79uxJ+sW6NXr27Nku8+SJtwuW7RyZE3dOAGqWlJQQy5T3Uk9YiQXpGnGeHpUjFPxZzn00Aa8cd7Gzyrk4AQCUh50joM7q8aHY593yAWLbmK7/FtvyfLWO0z+o7y32OS64R2zraTlHW/07mi/2KfDKcVh+Ie5EihkDgF1xOfqt3siRV1/wO8eG7YhliX0KvDVi27+izlFtWZa8L60qd64WCQAnZf3HcXqe1/k1BIByJZ6sd6jccfrBqNxnXyRbbNPixPIznLdTRUSOOztYJa+HJ1d4D1coBxmPfLyIZTi3SVGGwH9jEwW+OrmNKCU5vQWkt4zL+C8pH8jSIoWUBCgppkiLNooLcUiAHjUWFSKWbOWORC3mKS70ixr5Y2cUrY8a02Ot5I3r1yK0pBgylycObuLEvMqvaHFhP9Mi0jRR5XnJcWLaa6W8xkKb1keLrYtJ+4USGeYmGszt+0o/lrjoo0WNSS9/e69DigsEAiguLsaaNWuaRH2tWbMGF154oev5jh49GmvWrMGsWbMS01avXo0xY8a0aj68x5uIiNJPJ9/jvWTJEgwcOBChUAjFxcVYt26d+NiysjJcfvnlGDRoEDweD2bOnOn4uGeffRZDhw5FMBjE0KFD8fzzz7d+xYiIiFJZJ4/Xs2fPxsMPP4zly5djy5YtmDVrFrZv347p06cDAObMmYMpU6Y06VNaWorS0lJUV1dj7969KC0txfvvv59ov+GGG7B69Wr84he/wL/+9S/84he/wJ///GdxfJfwxJuIiEiRypmgRERE1GjSpElYvHgxFi5ciFNOOQVvvvkmVq1ahf79+wM49OX458fvESNGYMSIESgpKcGTTz6JESNG4Nxzz020jxkzBk8//TQeffRRDB8+HCtWrMDKlStx2mmntWrdeKk5ERGlnc68x/vwTFDgUJ7nK6+8gqVLlzpWVm3IBAWA5cuXO87z8ExQ4NA38G+88QYWL16Mp556qnUrSERElKKORE2WGTNmYMaMGY5tK1asSJpmhFs4Dvetb30L3/rWt9yt0H/xF28iIkpPbbxsrSW5oKmeCUpERJTyGP0JgCfeRESUjjopFzTVM0GJiIhSWiff453KeKk5EREdk1qTC5qqmaBERESUHnji7YInfujv8yJyOhC8LuJ3jPIBzA4qXwHFW38hg0e5iSIuxBd0CdaLfQJeOT6jZ4ZzvNa+qBzl1DUgR0rtjHQV24Zm7HScPiCwV+yjRXLtt51f5J6+CrFPjS1/mK+ynfMfdgjLAYC4Eq3Rx1cutv072sVxek+fHHdWrqy7tB7bYnK02sjsrWJbD1+l4/RNdQPEPrVK5pVXyNZ4v6Kn2Gdonvxr4+7aHLFtV7VztmQkKh9iY2Hl8Bt3fs+ZgBwXY9XJ8SnG7/z+DnymnORpTUo6jrJ7tqvOygVN9UxQap64rwj7jxjL01ybMD+jxokp47yLaKOY8gaMxOVjRMzn3C8cV6KhvPL8wrbzOBrxyH3UqDHLuV9EiSCrV+LEPGr0lnObrRxwbOX+0Liwo9nKT3l+LSZNWL+oi3U41E/eB6XtK8W7HZqfm1g45XUU9iUAiArvBe19EHPx/rFdvoe1NilmUBvX1DHPxfGss35NPhL3eKcqXmpORETpp5MuXTs8E/Rwa9asaXV+5+EaMkEP5yYTlIiIKKXxUvME/uJNRERppzO/QZ89ezYmT56MkSNHYvTo0Vi2bFlSJujOnTvx+OOPJ/qUlpYCQJNM0EAggKFDhwI4lAn6P//zP/jFL36BCy+8EH/4wx/w5z//GX/5y1/cPSkiIqIUxF+8G/HEm4iISDFp0iTs378fCxcuRFlZGYYNG9aiTNAGDbmg/fv3x7Zt2wA0ZoLefPPNmDdvHo4//nhXmaBERESUHnjiTURE6actl6C56JeqmaBEREQprZPH61TGE28iIko/HMiJiIhSH8frBJ54u+CtN/DayXuCJyJXL4xltX45nqjcphTeBmJCRWSvvPdW7ZdXMKOLc0n2vXVyn7yAXPG8PJLhOD3oiYl9PEpZxh5+52rYAFBrBxyn/62uv9gnX6iufWh+zlW0u/mqxT5epXpqyHJ+kQf4Dop9/h3tLrbVK1VhpWrt74X7iH2yPGGxTapOKj0nQK/wvjPazXF6b3+52Ocz5IltW2qcq5d/IVeuaP9JtVyR/WCdXGk+O+i8neoj8hvV45X3C7vOuZ8nLNfD9FfJbVKBV+HtAQCw5Lcj4srxJ1SefJyJR9p/5OQ9Y9RSVty5Er9TOgkACGETiXmJhDQCOHxeaKBWNRfmF1eSS2JK5fKIrbQJ1cvDXnlMqY3LB5Cg8AFGGkMBwKu8MaUq5F7tU7laPlgep2xhWX6tMrjSJlUUjyurHlC2RUS4miaqRFFIFfIBoEb53CB9htI+a2jjvPT6S8sBgLAtL0tqk/ZnAKhX2qT3T0x5z9lakpDy/paPF0oldOX4I7W5SWlQK6G7wPG6EauaExEREREREXUg/uJNRETph5euERERpT6O1wk88SYiovTDgZyIiCj1cbxO4Ik3ERGlHd4zRkRElPo4XjfiPd5EREREREREHYi/eBMRUfrhpWtERESpj+N1Ak+8XbBs51L7PufULQBAzDlBCwAgpTIo6VqI+pU9UWiypOgCAN4cOVqjvtY55iEckqOm6pUIknjU+UKLXhkVYh/NASWrze93zleQok4AoCIux0YV+Kocp2uRYfVGjsnYHXeOwyq35XUIKDlPO2NdxTZbyJTK8cg7rhYNVm9nO07/NCJHcmmxcLsjXcQ2SXVM3rYZXud131JeKPYJeOWsjq4ZtWJbWIgniUTk90EgJL+O9QedI1c8YSWaRIn/sIPOBwXjkefnV45nqYCXrlFLSWO29J5RI3tcRI1ZQsQnABgtpijm3BaNKbFgPrlNOk4BcsRSnZIdGPRocWLOx7eQMn55lY0rjbFaH+2YqF3vGTXOL6RfWZZfOahEpTxHRViIDAOAuLDy9ULEZ3NqlCivGuHzS70t7xdaZJwYJxaX+9QpsXVSmxYZFtEi94S2uK3FiWnvby0azLmt3Y8/Sh8pUlF4C7jG8boRT7yJiCj98Bt0IiKi1MfxOoH3eBMRERERERF1IP7iTURE6YffoBMREaU+jtcJPPEmIqK0Y/33z21fIiIi6ngcrxvxxJuIiNIPv0EnIiJKfRyvE3iPNxEREREREVEH4i/eLkhl8b31ch8tGswSUrniIbmPt9ZFtIFH/too5pF3BW+G88qHY3KfnQe7iG1dspxzij6rzxX7hIRoKAAI2/J6+IV8hTolPqOrr0ZsqzfOERpa7Ja0DgAQEmLNPo3JkVxF/gNimxQzAgBdvM7PS4tC+yDcS2yTotXiyoVBmcp26hM46Di9VnmtNFtrujtO1yLDfEruxq4q5+g3AMgWovUs5T1XXy3HpyDgvB62Emki7JoAAF9162NLtAScgPNLDwCwvcnLcprWVownoZay4s77uhSlY2txPmqb8D7TEq+UuCEpTiyuRJCpUWNKzKcUAVqvxInVeeUPNj4hHkobD9tb3CNvJ22c8sN5HQPKumvPK+oi5svjIp4sKmXTNkOKDAOAqrhzFq70WQgAqmz5w6sUG6Z9JqtW4sRqhUhRLU6sPiavu/T+iQvvRUCPBLSUftLxR4sf1I8/ndPHDY7XjXjiTURE6YeXrhEREaU+jtcJPPEmIqL0dJQNyEREREcljtcAeOJNRERpiJeuERERpT6O141YXI2IiIiIiIioA6XliffBgwcxefJk5OXlIS8vD5MnT0Z5ebna56qrroJlWU3+Ro0a1TkrTERE7cu08Y86DcdsIqJjGMfrhLS81Pzyyy/Hf/7zH7z88ssAgO9973uYPHkyXnjhBbXf1772NTz66KOJfwcC7qoleyIGXpO8J0QzlCqZ1fL8YpnO07WqwuqlF8Jq2D65k+WV27p0qXWcHreVyovKCuaFnKuaa1U8tbbqqFxBc783y3F6UCkzvy+aLbb1ClQ4To9b8ouVaUXEtr2xHMfpWuXyk4K7xLa1tV8U2+LG+fXSKqEeiMnbQuoXsuRtq1VC3VzZz3F6QHmtyiPCmwdAQCgZqlUu1/azrKD8OtZFnZ9XtF7etiaiVUJ1fq38VUqV3qC87j7nt5yaxOAV0hYAwLKV96rTyxVt/5GTl66ljyM+ZscNPPHkF90SxjA3VYAPLcd5utFSTZQKxvA5t2kVlqNepaq5T24LC1Wga5UK0AGtqrmwoYIe+TX0auXfXdBSPmylzS+MYX4jv/haxfOIi6rm2raIS1XNIS9H6gMAtbacsCFVKK+35f1Cqlx+aFnOr3+1UJ0c0CvrS9XLpf0ZACJxeTtJVc2lhAEAgJJMIBTIV/tJxxHA3fFHn5/zYChNd4vjdaO0O/HesmULXn75Zfz1r3/FaaedBgB46KGHMHr0aHzwwQcYNGiQ2DcYDKJnz56dtapERNRRWCU1LXDMJiI6xnG8Tki7S803bNiAvLy8xAAOAKNGjUJeXh7Wr1+v9l27di169OiBL37xi7jmmmuwZ88e9fHhcBiVlZVN/oiIiKhlOGYTEREdknYn3rt370aPHj2Spvfo0QO7d+8W+02cOBG//e1v8dprr+Huu+/Gu+++i7POOgvhsHw95aJFixL3pOXl5aGoqKhdngMREbVNw6Vrbv+oc3DMJiI6tnG8bpQyJ97z589PKqTy+b+NGzcCACwr+b4IY4zj9AaTJk3Ceeedh2HDhuH888/HSy+9hA8//BAvvvii2GfOnDmoqKhI/O3YsaPtT5SIiNqOxVqOKI7ZRETUIhyvE1LmHu8f/OAHuPTSS9XHDBgwAH//+9/x2WefJbXt3bsXhYWFLV5er1690L9/f3z00UfiY4LBIIJBuUgEEREdIbxn7IjimE1ERC3C8TohZU688/PzkZ+f3+zjRo8ejYqKCrzzzjv48pe/DAB4++23UVFRgTFjxrR4efv378eOHTvQq1cv1+tMRER0LOKYTURE1Dopc+LdUkOGDMHXvvY1XHPNNXjwwQcBHIom+frXv96kOurgwYOxaNEiXHTRRaiursb8+fNx8cUXo1evXti2bRt+8pOfID8/HxdddFGr1yEetIBA8iVyTnEliT5SxpdCiw3QosE8YedlCSkOAACjRCWUV8iRTRJfQInWEKIcdtR1Eftk+uUop5O6lolt1XHnJ63GiYXlCK3jQ87FfbSYrM9iuWLb7nCe43QtTmxV9TCxrULKpgOwz3KOLgt5omIfKfoDkONOquJyvFtNTP41qkewynG6+npk7xPbSvb3dZxer8TjVNfL61cflvtF64Q2tzcnSW9HZXa+WiXeT3o7KvPTkn20Y5Ov1mGmjBM7ZqXCmG3FnfdZaRjQ4ndsF1E/lhI3pMWJSRFGthL/GfcpUWNCVBIA1Hucj2F+ZWPUKhFQHuHg4ncZGabFYbnpI8VrAnI0mBQzdqhN3k5RV3FiymssrHu9cRe3p43zVfEMYVny6UO1EidWJ3wmk6YD+n4mxYnVCxGfgP4+iMeF95wWJ6a8h7X3vnT8USPDtGhC4a3lKgJRi0FzgeN1o5S5x7s1fvvb3+Kkk07ChAkTMGHCBAwfPhy/+c1vmjzmgw8+QEXFocxlr9eL9957DxdeeCG++MUv4sorr8QXv/hFbNiwATk5zicjRESUwnjPWNrgmE1EdAzjeJ2Qdr94A0C3bt3wxBNPqI8xpvGVysjIwCuvvNLRq0VERJ3EMgaWcTciu+1H7nDMJiI6dnG8bpSWv3gTERERERERpYu0/MWbiIiOcaySSkRElPo4XifwxJuIiNIOi7UQERGlPo7XjXjiTURE6YffoBMREaU+jtcJPPF2wRs28NnJe0JdtnzLvFdOw4ItJBtoCRT+aiWCREhe8FW1PtICAOIh5/wCo8RxxJQ3yv6arFbPT/N+RaHY1iOj2nH6PmmjA7CV6Le/Vxc5Tq9RojD6hMrFtu7+Gsfp/6hzjsICgG4+5z4AUBmTo7wGhPY7Tt8e7ib2yfPViW1u4l08SpSMFBt2ICxHpP2nxjmODQCiwmtcWSdvo0hEPiTaQswIAHiF+Lx4ROmjvB+lyBDtmOCtl9sgxYxo8WR1cqPtU96rTjN199YmahdW3MDjMChJUV5KwiI8yntQSljShjbbIZq0gRVxbjMe+bgSU1Yw7JHf05ZwMPBYcjSUxnYxnkeVMSXsdd64WlRXvdAHAGpt+XkFhR3AKx1I0RFxYvKypLFXW05cKemkxYnVCtFgYVvetuVRecyuizvHfFUrUaPVUWX9hLb6qLx+YaUtFnHehiYqbz9LGec9wnsYADxRF8cfF20eJc5T+qyhxSZS2/DEm4iI0g4vXSMiIkp9HK8b8cSbiIjSDy9dIyIiSn0crxN44k1ERGmH36ATERGlPo7XjZjjTURERERERNSB+Is3ERGlH166RkRElPo4XifwxJuIiNLS0XYJGhER0dGI4/UhPPF2wRsx8JrkPchbL+9VxqtECkjRQWF5HbQkJzHVQkm0sIPKO+KgEOXQRc41MLb8fKXYsJgS1xSOySvfNUOO3aiMOEdHVQjTASAnIG/4QIbzi5XhlbdFj0Cl2LY70sVx+mf1OWKfzBxlx1BsquznOL1XqELss7U2X2yTYr6Oy94n9tkTlp9XSNiGVVElZiQst2UHnbdTQbZzxBwAfFYpr1+9EDMCAHbYuc3SIkjk3VaMOdIoiTDwC09ZiyaJZsnrkF2mZI04HEq0OBPXjDn057YvHTM8Uef76pwixgDAKO8/j7Lr28JYrkWQae9BeJzXw1aOK8Yr79tSVBIAhKU4MRcRZBqP0keL8owJUVkxJRpUi7zKVDJe/cLBVIsM06Iy7XaO3pRiw6LK89VocWI1QsyXFv1WpUSD1UtxYi4iwwCgLuo8PzUyLCrvMybm/Ly0sdyjHC+0sdwSjhfSdED5fA/5XEI7Zkljc7uP2RyvE3iPNxEREREREVEH4ok3ERGlnYYqqW7/iIiIqOMdifF6yZIlGDhwIEKhEIqLi7Fu3Tr18W+88QaKi4sRCoVw3HHH4YEHHkh6zOLFizFo0CBkZGSgqKgIs2bNQn19favWiyfeRESUfkwb/4iIiKjjdfJ4vXLlSsycORNz587F5s2bMW7cOEycOBHbt293fPzWrVtx7rnnYty4cdi8eTN+8pOf4Prrr8ezzz6beMxvf/tb3HTTTbj11luxZcsWPPLII1i5ciXmzJnTqnXjPd5ERJR2LFu/T765vkRERNTxOnu8vueeezB16lRMmzYNwKFfql955RUsXboUixYtSnr8Aw88gH79+mHx4sUAgCFDhmDjxo246667cPHFFwMANmzYgNNPPx2XX345AGDAgAG47LLL8M4777Rq3fiLNxEREREREaWkysrKJn/hsHMB3UgkgpKSEkyYMKHJ9AkTJmD9+vWOfTZs2JD0+HPOOQcbN25ENHqoAubYsWNRUlKSONH+5JNPsGrVKpx33nmteh78xduFWIYF+JMrFYYOyl/LxDK17ziEyqXKq+NxUfFcu09Cq4RqSRXKy52rSQIAuskVQ2tqnCteen3y9vP75LKMB+ucq2sDQMDnXOYx6JXLRpbXZ4htEp/yldzO2jyxrUfIudx0lk9+gTeV9xfbMn3ydpfmuaOuq9gnP1AjtlVGnSvDH4hkiX3+XS5XSc8L1TlOr4nIFU0z/HJJ4P3VzusRV6rnR+qVN53y/vHUKmWLBW6+xfU5b6JmSccSqQoqAASqlOrDSkqDN5L8xCy7I6qag7mg1CKemHGspu2Nuhh7lSrkXunQogz/noiSACI0WUrogfHIC1PCRiAVX27d3YuHrYe08opIXD6ORnzOL0rYK79YWlXzurg8rkifDzxQPqMo5aalKuQatfq7sG215Uh9AH1b1AlVyCPKtq1Ukkik11irXF4bkT9rRoTq5bGIvH7xiPKGDEtVzZWkA/ljF5Ti+eKxRDvG6G2tr1AuJTtI011rh/G6qKioyeRbb70V8+fPT3r4vn37EI/HUVhY2GR6YWEhdu/e7biI3bt3Oz4+Foth37596NWrFy699FLs3bsXY8eOhTEGsVgM1157LW666aZWPR3+4k1ERGmns4u1pGqhFiIiolTWHuP1jh07UFFRkfhr7t5q63PfUBpjkqY19/jDp69duxa33XYblixZgk2bNuG5557Dn/70J/z0pz9t1bbgL95ERJR+OjEXtKFQy5IlS3D66afjwQcfxMSJE/H++++jX79+SY9vKNRyzTXX4IknnsBbb72FGTNmoKCgIHG/WEOhluXLl2PMmDH48MMPcdVVVwEAfvnLX7p7XkRERKmmHcbr3Nxc5ObmNvvw/Px8eL3epF+39+zZk/SrdoOePXs6Pt7n86F79+4AgHnz5mHy5MmJ+8ZPOukk1NTU4Hvf+x7mzp0Lj3K10eH4izcRER2TWnrP2OGFWoYMGYLFixejqKgIS5cudXz84YVahgwZgmnTpuHqq6/GXXfdlXjM4YVaBgwYgAkTJuCyyy7Dxo0bO+S5EhERHe0CgQCKi4uxZs2aJtPXrFmDMWPGOPYZPXp00uNXr16NkSNHwu8/dKtDbW1t0sm11+uFMSbx63hL8MSbiIjSTntculZUVIS8vLzEn1O101Qv1EJERJTKOvvWsNmzZ+Phhx/G8uXLsWXLFsyaNQvbt2/H9OnTAQBz5szBlClTEo+fPn06Pv30U8yePRtbtmzB8uXL8cgjj+DGG29MPOb888/H0qVL8fTTT2Pr1q1Ys2YN5s2bhwsuuABeb8vrOPBScyIiSj/tUKxlx44dTS5dCwaTiwKleqEWIiKilNbJxVAnTZqE/fv3Y+HChSgrK8OwYcOwatUq9O9/qDhxWVlZk0zvgQMHYtWqVZg1axbuv/9+9O7dG7/61a8St4YBwM033wzLsnDzzTdj586dKCgowPnnn4/bbrutVevGE28iIko7br8Jb+gLtPyeMaBjC7Wcdtpp+Pjjj3HDDTegV69emDdvXkufChERUUprj/G6tWbMmIEZM2Y4tq1YsSJp2vjx47Fp0yZxfj6fD7feeituvfVWdyvUMJ829T5GBcvj8DnEW0Wz5Cv3fXVK1FhIiC8QYsYAfUcUI4LUKCJ53eNB54WJMWMA7Go5/sGWosuy5JyE6irn6CoAiGfJeQ11QgxFTImU6pIlbygpaqxnVpXYx47L26k25hyhUR2T4zjqY/Lbdm+dHOUVFKLVMn3ydv9PXRexLeBxjk/ZVSufyHg98vvggBALF/DKMS37q+TnG406X/oTq5H3TU9AXhbK5bgT43Hep33V8uVHXiUS0F/pPD3SRe7jk5Pf4BfaAtVKzIgSQeIUGdbA6djkduBMBaleqIWa540aeB1+NrEjzjumklAF41Hiv4S3u9EihbRPYdIXO8quYVtyo/Y2VI58ruZnC58PtFirqBIPGbGdN25IebHqvfKxPqBEivpizsc3vzDmAYBH2Rq28lmuPecXFbYRoG/3eiEy7FCbENcl5dYCqIoocWLC55dwTF73eiVOLCaM8/GIPD+jxIl5hDYt9k9t0+K/hOOC13WcmDA/NdKs9RFk1DYc2YmIKP00VEl1+9dCqV6ohYiIKKV10nidDviLNxERpZ3OvHRt9uzZmDx5MkaOHInRo0dj2bJlSYVadu7ciccffxzAoUIt9913H2bPno1rrrkGGzZswCOPPIKnnnoqMc/zzz8f99xzD0aMGJG41NxNoRYiIqJUdiQuNU9VPPEmIqL004nFWlK5UAsREVFK6+TiaqmMJ95ERETNSNVCLURERJQeeOJNRERph5euERERpT6O14144k1EROnHNof+3PYlIiKijsfxOoEn3i5YcQOrlV/BxANy3ICv3nm6ktaAuJzWgLiQeGHk5CU12sgTdV73SBc5UghCvBIAWD7nfnZMfsKBDDlDobZa3hg5uc7RYFq0xsFq51grAMgMOecylFXLEVoBIcYLAKqizuue5ZfzH/bVyC9kj6xqsW13TY7zsgLysuK2/JrURJzjtbT4L011nfO2iNTJUSL+oLxtpf3JG1L6VMqRYdpb3lsnbCelk69WiSUSZpe1S16HSLbc5q91Xg/tGKMl4KhRY/UO7++Yu31CxXvGqIWsmA0Lyfulx++8k2uRPV7lPWO8zvNThht1WdJ7UI00U5ZllKgxifbO1YoNG2FFpOkAEFPGm4gQGxZWxtd6JTJMisME5DHMox3PLSUyVj3QOnMTJ6ZtP+0zjxTVBgB1Mefx181nAwCIC1Gu4ah8OhJTosHsqLAeYXn9LOEzrdbW3pFhgBwbph5/tLFXjAaT900xTizWzoMkx+sExokRERERERERdSD+4k1ERGnHQhvuGWvXNSEiIiIJx+tGPPEmIqL0Y4x+rWtzfYmIiKjjcbxO4Ik3ERGlHVZJJSIiSn0crxvxHm8iIiIiIiKiDsRfvF3w1cbgc6ikaQsVUgEgpnzHEc5y7mfFtcrB8rKkiudeoXo6ANhyEUrElTaJt0KpQhl03hYmID/fSK28q1pZcgnIyoPOFcD9SpX0uFJdXapqvme/c8VwAOjatUZsy/A7r0dZlVwl3euRK1Rq1dWlZdVHlarhSoVyqcJrOCa/9uGIvCyJsZVqrAdCYpsVcX4dbZ/y9alSjd9XLT8vqaCtVtE0JhfPR6Dcebr2XgxWKMsKOm9Df538fD0RpU2peOqJJu8zHlY1pyPIG7HhtZPfpMYvjEVa5XKlorhHOERo89MSRcR1UG96dHdHpBFWUnuraCk/UeG4rR3Po8rYEfU5H0MicbmPVAkdAHzK2CZVKNfGXq3iuVZR3M38pOrlWsV4qRI6AESVbRiOOW/DuPI6auO8VNU8LlUnB2BH5fUzQj+PVtU8Jq+7N+zc5lXGcm2cV9ukquZaJXR1WUKFcm0sjzjv056YklrkBsfrBJ54ExFR2rGMgeXy3i+3/YiIiKh1OF434ok3ERGlH/u/f277EhERUcfjeJ3Ae7yJiIiIiIiIOhB/8SYiorTDS9eIiIhSH8frRjzxJiKi9MNiLURERKmP43UCT7yJiCj9GHPoz21fIiIi6ngcrxN44u2CpzYKjzf59nifEE3SnEClc6xFXYH88mjxJHEhOiguJy+p8QVSYYPgAXklInnyG8WKC/FptUoURkiprqAldVQ5b0M7mBwH18Dnl2NG6iPO8/OH5PlV1wn5bgAqqjIcp3uUWKtgQF6WFsdSF3aO+IgL0SSAHJ8GANU1zs8rrkR/5OTWiW0Ve7Idp1t+d5U17Ezn19Er7BMAYMmbVt3PpDgxf5W7+QWEfrZyxLaUxC5LyP3xROX9zF+tRMlF5dfEcogac5pG1Fk8ERsehzgxj3Bs8XrkY6JRjs3iuGzJb3YjHy7l2DB3iWFqRykazFY+bGjRYFK8qhQzBgBxn3xckWKo3ESQAYDXKy9Lig3zKD+9eZX9Qovekii7jHgeEtc+GCrUbSi0aRFpsYgSJyvFtSoxrhCiQQHAE3VeD09EXj9L6HOoX+umA3rEl1dOrhXn6VXjv5R9UBjPvcp47RT/CXRQBCgBSNPiarfddhvGjBmDzMxMdOnSpUV9jDGYP38+evfujYyMDJxxxhn45z//2bErSkREHcIybfujzsMxm4jo2MXxulFannhHIhFccskluPbaa1vc54477sA999yD++67D++++y569uyJr371q6iq0n6SIiKilNRw6ZrbP+o0HLOJiI5hHK8T0vJS8wULFgAAVqxY0aLHG2OwePFizJ07F9/85jcBAI899hgKCwvx5JNP4vvf/35HrSoREXUAy5Yv8W9JX+o8HLOJiI5dHK8bpeUv3q21detW7N69GxMmTEhMCwaDGD9+PNavXy/2C4fDqKysbPJHREREHYdjNhERHY2OiRPv3bt3AwAKCwubTC8sLEy0OVm0aBHy8vISf0VFRR26nkRE1EK8dO2oxTGbiOgowvE6IWVOvOfPnw/LstS/jRs3tmkZ1ufKRBpjkqYdbs6cOaioqEj87dixo03LJyKidmLa+EdtwjGbiIhahON1Qsrc4/2DH/wAl156qfqYAQMGuJp3z549ARz6Fr1Xr16J6Xv27En6Rv1wwWAQwaBDZJIHjl9ZaBE7/iq5LdzdOZbJeOQPGL56eU+UIof8tWIX1OW7iLtQ0gb8la2PT1FjVXzK/MoDYpsn5tzPCJFmABCuluO/wkKEhuVVjgxKRIpPiDWL1DlHfwFAtF5+2wYy5ewKaZ4BJQqt/ECW2AZhG/qz5HWo3C/PT9qGRokmsZRIEyssvFZKvIf2VaSvRuknrIYW4edX5hdxTlZDsELez7RjQqDaeR/U7p3yxJVlVYbFNsshnsTEtbxCdyxjYLn8JtxtP2qUTmO2FY3DspP3S48wriiHFXi1mCeHmNHmaOO8K8qurVUHtqTIK+UYob2NbCH+S40gU8ZlO+o8Py2CLOZTYqiUMdsjbChL2YBam9F2qHacnxbxpYkrUV5S/Jf2OholUlT67KVGfCltUj+vMP4DemyoVxjavPVyH4+LyDAA8IWdX2MtTswbUaLBwkIMntYn0jlxYhyvG6XMiXd+fj7y8/M7ZN4DBw5Ez549sWbNGowYMQLAoSqrb7zxBn7xi190yDKJiIiOVhyziYiIWidlLjVvje3bt6O0tBTbt29HPB5HaWkpSktLUV1dnXjM4MGD8fzzzwM4dLnazJkzcfvtt+P555/HP/7xD1x11VXIzMzE5ZdffqSeBhERucV7xtIGx2wiomMYx+uElPnFuzVuueUWPPbYY4l/N3wj/vrrr+OMM84AAHzwwQeoqKhIPOb//u//UFdXhxkzZuDgwYM47bTTsHr1auTk5HTquhMRUTswUC+DbbYvdRqO2URExzCO1wlpeeK9YsWKZvNAzee+IbEsC/Pnz8f8+fM7bsWIiKhT8J6x9MExm4jo2MXxulFaXmpORERERERElC7S8hfvI85jAZ7k7yximfLm9CtVgD0xobKhUPEQACyl4nCg2nl6XC7+DX+1Uk1U6BeXC2/Do+xZsUzn6VqFZW+9VqFSbot2ESo2fiaXm/YpX67F853LV1oV8hM2ufIMY2Ghn1b5VakYGrZb/11afZVSgVTZtlIV8kiFXBVerVxaL1RP9SvvA239hKKcvjq5T6BcbEJcflpiJVSNV6t2KlRd1Sog28r70RaqN3vrlIr71XKpVuNw/GtgOb2RlQgo1wzc3/t1dH2BTs3wROLweJPfVEaqeq28z7T3oNfT+h1LS/MQ4xK0Hm73bamfUinb1pYljGFG6aSmlwgDs1Q9HQDsmHx8s5TXSmqztOFV2/Buqo1rVc2lzwcuX3upcjkAQKxOL3exIko1eamquTKWq1XDhc8UWjVxj4uq5to6aOO/XqG89Z/9PS4qnkuVywHACju3WXG314ULOF4n8MSbiIjST1uKrhxll64RERGlLI7XCTzxJiKi9GPDzQ+CjX2JiIio43G8TuA93kREREREREQdiL94ExFR2mGVVCIiotTH8boRT7yJiCj98J4xIiKi1MfxOoEn3kRElH44kBMREaU+jtcJPPF2wVN2AB5PcsZWqDJL7BPtmSu2BffWOS8nV84vimUqERpKJIdEi/KyhOgFLVpDi2uQ4lOk+Kf/toot8ZASrXbQeWGxTC36Q1mNajX7xZGnXM55sv3ChlfiR7xK7EZciSCRIj60GA+vEv8lsZX4L2+tEkMlbYqIEjEjRJoBQGi/cz8tVk977X3Ob1MAcvKLV+mjxYwEqoU2ZQDyVytvICHOy1uv9FGW5a1SnlhdffLibRd5a0TtxKqLwPImvwc8wvtCvbRRaZKOA5YSD6mV2pHGRG1+ce0woLRJcYRSnCgA2MrYYQtDpR1wdzw3wqdVo8SCiXFxAIzy+UWap7YstXCUi6g2N/FkapSc1iZEfAHy5wN1UyifGyxhWWpkmPJ5UurX3nFiWsSXFg2q9xPixOrlD+TamO2td35injp541ph5zZPXHlS1CY88SYiovTDb9CJiIhSH8frBJ54ExFR+mE8CRERUerjeJ3AE28iIko7rJJKRESU+jheN2KONxEREREREVEH4i/eRESUfnjPGBERUerjeJ3AE28iIko/tmmmjG8zfYmIiKjjcbxO4Im3G7EY4GndVfq+AzViWzwnw7lPrZx5YLxyRJUUyREPyuvsr5F3bFvYS7RIEy2CxF/tPF1L1pCiTgDAW6dEqzhvWmTslvtEusjLsqJCRoqWraE8MeMRojWUCC07KC/LV6G8pcWoG7mLuu7CfuavUqLulKgxKWbEXyl2QSxTXj8pZkSLkdFqf4QOyOsezXLuGayUN66+3aU4G3fVSaQIEil+BAC8B2vlGSrrYXIyk6fFWx/D1yx+g04tFY04RiZZPul4Ls9KiiA7NEOpQd7/1YgqN5Rjthob6mZ80OYnfW7QhkqHyLfEooRDlRRPCgBGiTuDFl0mxcwps3ObDNau83O5K0ljL6DEySqf/7RoMGl/kpYD6HFdUj+vFk+mtQnLau/IMADwhJ03hjcsR4Z5lDYr4rwxpOkAACFODLaykdzgeJ3Ae7yJiIiIiIiIOhB/8SYiojTUhm/Q3f40RERERK3E8boBT7yJiCj98NI1IiKi1MfxOoEn3kRElH5sA9ffhB9lxVqIiIhSFsfrBN7jTURERERERNSBeOJNRETpx9ht+2ulJUuWYODAgQiFQiguLsa6devUx7/xxhsoLi5GKBTCcccdhwceeCDpMeXl5bjuuuvQq1cvhEIhDBkyBKtWrWr1uhEREaWsTh6vgdQds3mpuRuZIcATTJ4el8v8wyPnYXnqhLL9Pvl7kUBEXpa33nlZVlx+ueMBeVlS/IMWQRbNlqMmYhnObTGHTdogeFBu06LGpHXX+vjk5Df4hISlSJ4SraEkOXhizts9HpC3bXCf/Fqp0SrCKmpRJ/GQEpMRFuK/qpT5BVofxWMpb6vM3XKb9Br7lddXixmJ5MjrLkWNRHLk1ypY0fqoMX+NvDH8lfLKe2udV9AoxxgTkHcmq0LeiJbDcdCylSwWtzrxnrGVK1di5syZWLJkCU4//XQ8+OCDmDhxIt5//33069cv6fFbt27Fueeei2uuuQZPPPEE3nrrLcyYMQMFBQW4+OKLAQCRSARf/epX0aNHDzzzzDPo27cvduzYgZycHHfPiWT1EcefGSxv62PuXP1a4S5tUoxssuKtH68BwFaOpXEhUspSokHVZQmbVouN0sYvj9CmRZBp0ZGu+imDZUrEiSkRXxqPsl+I46/ynLToLSmCTo34Uj9DCdOVdfDElEjWsPN0PTJMfiNIkWFaPy0yzCPFfwGwpHjQemVjhIUn3N5jdiff453KYzZPvImIKP104j1j99xzD6ZOnYpp06YBABYvXoxXXnkFS5cuxaJFi5Ie/8ADD6Bfv35YvHgxAGDIkCHYuHEj7rrrrsQgvnz5chw4cADr16+H33/oW6L+/fu7ez5ERESpqpPv8U7lMZuXmhMR0TGpsrKyyV/Y4dv/SCSCkpISTJgwocn0CRMmYP369Y7z3bBhQ9LjzznnHGzcuBHR6KFfLP74xz9i9OjRuO6661BYWIhhw4bh9ttvR1y7coqIiOgY1JLxGkj9MZsn3kRElH4aLl1z+wegqKgIeXl5iT+nb8L37duHeDyOwsLCJtMLCwuxe7fzvQ67d+92fHwsFsO+ffsAAJ988gmeeeYZxONxrFq1CjfffDPuvvtu3Hbbbe2xdYiIiFJDJ43XQOqP2bzUnIiI0o9BG+4ZO/SfHTt2IDc3NzE5GJQLTVhW0/snjTFJ05p7/OHTbdtGjx49sGzZMni9XhQXF2PXrl248847ccstt7Tq6RAREaWsTh6vgdQds3niTURE6acdirXk5uY2Gcid5Ofnw+v1Jn1TvmfPnqRvyBv07NnT8fE+nw/du3cHAPTq1Qt+vx/ewwp8DRkyBLt370YkEkEgoFS1IiIiShedNF4DqT9m88TbBVNVA+NQgtEKhcQ+avVUqXqwUGUUAOCX52cHnL8F0iqQ+qvlexSkCpqRXK2EttwUOuC8InX57u58UKthCm1aVfOY/DK6Woe4Mj+pnyfisjqpVohSqhqu7BeBCq06fevXwSsU0NRoVXD91fKOZvud1912edQLlSuVS4V11N5X8Mjb1lflvGN4osqLpewyUvVyz4FquVNM2fC2vB52RWXyNNMBVc07SSAQQHFxMdasWYOLLrooMX3NmjW48MILHfuMHj0aL7zwQpNpq1evxsiRIxNFWU4//XQ8+eSTsG0bHs+h1+fDDz9Er169eNLdzkwk4lglWhqX3R195Xv3LO0Dp7KwuO08R61KtlQJ/dD8lF97hLe01kerNi0dZ7XK6lIldECueK4meWhtWsVz8YV0u2d0Dm0sV/u5qGquLUv7PCT108Z5rzY/oZ83Ir9JtKrmUvVybX5epXK5R6147rxxXVUuB2CFhXFWqlwOwAhtpiOSSDpJqo/ZvMebiIjSj2237a8VZs+ejYcffhjLly/Hli1bMGvWLGzfvh3Tp08HAMyZMwdTpkxJPH769On49NNPMXv2bGzZsgXLly/HI488ghtvvDHxmGuvvRb79+/HDTfcgA8//BAvvvgibr/9dlx33XXts32IiIhSQSeO10Bqj9n8xZuIiNJPJ+aCTpo0Cfv378fChQtRVlaGYcOGYdWqVYkokbKyMmzfvj3x+IEDB2LVqlWYNWsW7r//fvTu3Ru/+tWvErEkwKFCMatXr8asWbMwfPhw9OnTBzfccAN+/OMfu3tOREREqaiTc7xTecy2jHG7JY49lZWVyMvLw1e6XgmfJ/myAu1Sc2Rlik1GutRcuazJKJeaR/KdlxUPyhc4WMqlN24uNY9mKpfR1jvP0O2l5m64vdRculQ6Jr+8+qXm0lVDLt+V2iVjbi4199bLbdKl5r5aZRVcPC/tErRAVeddah6sSPFLzRWesPMKdsil5uUVybMyEbxW+zQqKipadI+WpuE4fHb+1Y7H4ZaI2RH8ed/ydlkfSl2JMbvLFPgshzE7UziIheSiPSYo73Mm5HxwMQH5oBPPUNoCzmOirYzlceG4BwDxoNwmHS+1+RnlWCpeaq6Mval/qbncJxXwUvPD+vBS80Z18gc56VLzmB3Bqwcfa/MYyfE6GS81JyIiIiIiIupAvNSciIjSj23g+tIQmxd6ERERdQqO1wk88SYiorRjjA1j3F1b6bYfERERtQ7H60Y88XbBsjywrOSr9E1tndxHuWfMqhHu2fApNyh55LsEvHXC/ZwR5b4w7f5v4cumQIVyU46ya8UDzjdKqdFQPu3eNHkt/LXO89TuQXfzpZx2j5S/Sm7zCbuMdq+bR4tjUbZF3MXtNdrzCiSnRjXbR7svTFp3r5JqEctofdRNQNnPPFG5TapNAMAxqggAjFeJ74kr94zVOq+8GkuktIk1IbRjTJVy/7dXPl7YDveT2Ua5Sc8tY9x/E87SJscUEw7DOA1kQp0F7VZeV7f5avfDahFVwv6tx4kpY7l2/JWiLZVxI66MN5YwZruJIAPk+661sVK7mVLtJ70k2scGpc1NbRNX89OWo+4zSpt0j7cyPzf3eKuxsMo92dL+JN2rDQAebeytd15B7bOBV7hXGwA8ESWqNyKM89p93HVKJmvE+cOScXGPt2nvCFCO1wm8x5uIiIiIiIioA/EXbyIiSj+mDfeMHWXfoBMREaUsjtcJPPEmIqL0Y9vu83OOsnvGiIiIUhbH6wSeeBPR/2/v7kOrrP8/jr+OupvMedTmPMfQaVkTsUJdtlneTfKOyqaJmoxJEBWIWFKYUeofpoYZgaV8QdSoSEiNxJCENk1cuXTSSryBphv8Wubdtkw3t31+f5jHzZ3rcud4rp1zXXs+4IC7bs55f87bXe99zs3nDbgPr6ADAJD4qNchfMcbAAAAAAAH8Y43AMB1THOzTJQfXfNaexIAABIV9foWJt5RaLx4UfK17aPh62rdn6KrzT7de4/VWZanWLUhkKSu/4b/IIPpZtOC7Jp17wpj0e6koZd1nxG7VmNWLZbsWppd6229L8WirZVk3ULLqs2YJHW5bteiKvx5tufYdVKyOK1blNeZRrsWJBZdLZJsukbZtSezbK0S4zYjdu3JUmqtnyirx7JqS2MXgyR1qbfemfRP5O2yfDYtUrr+E779h9XvoiT5mq3jM//3V/gdfXpZnmPVakmSmi/XWJ8Xrkg6UTj56BraqfnqNTWHuZBYXgps2t74mmzaA1ns8zVa10q7FoG+xvB/otm1V2q+btNOLNl6n0kKv6/Jpqh0sW3zGT5Gu9agxubPpGaLvxvszrG71tueF0U7Mdt90Vxuork/u5ZhsW4nZlcrbf5/Wt2fbcuwKFqNdbVp/+W7bh181waLdmIxbhlmu++aTcswm32mPvJ2Ys314ffFvAUo9TqEiTcAwH2aTXQNciXPFXIAABIW9TrEld/xXrVqlcaMGaPu3burV69e7TpnwYIF8vl8rW45OTnOBgoAQCdHzQYAwKXveDc0NGj27NnKzc3V5s2b233e1KlTtWXLltDPycnWH/8CACQwYyRF257EW6+gJzpqNgB0YtTrEFdOvFeuXClJ2rp1a0TnpaSkKBAIOBARAKAjmWYjE+VH14zHCnmio2YDQOdFvb7FlRPvaBUXFysjI0O9evXS+PHjtWrVKmVkZFgeX19fr/r6WwsZ1NTcWFCoUdfDrhHgs1lAyDSHX/RAktRs8Yn/JrvVMKxXBmm2OM/YrdZhs2iT1YJOjTYLVNgtGGOaLRZX62L9zYemBptvRdisAWEVod3CIE2WK6tIxmIhj6Ykm3OiWFwtysUf1RTFgjFd7P5r2l3volhcze65sFrsxm5xNbv/g7FeXE3XbRZQaYzt4mpqCr+AStSLq5nwSfY12yziYnPNslt4Jdy+xv9+SWNaQE2zon8F3VurpHqV0zW7i8VFx2dTA2yvEVb7bGq5sdnX3BR+8SXTaFP/7eqozT5j8c3DJpu/G5ptnierp8Kq/ksuWFzNTiIsrmZ3dx24uJrV30l292f1d6sU3eJqxm5xtUabWmmxr0ujzeJqUSy4eGOfxeJqUdZlqzpvtV2yruUxr9nU65BOM/GeNm2aZs+erczMTFVUVOjdd99VXl6ejhw5opSUlLDnrF69OvRKfUsH9V34B7GZIOhilPsAwCl1HftwFy5ckN/v79gHhSt1SM2+avHgVtsBoBOhZsdewky8V6xYEbZgtlRaWqrs7Oyo7n/OnDmhfw8fPlzZ2dnKzMzUnj17NHPmzLDnvP3223rjjTdCP1++fFmZmZmqrKz05H/E2tpaDRgwQFVVVerZs2e8w4k5xuduXh6fl8cm3XjnceDAgerTp0/M7pOPrsUXNTv+vH7d8PL4vDw2ifG5XaxrNvX6loSZeC9cuFBz5861PWbQoEExe7xgMKjMzEydPn3a8piUlJSwr6z7/X5P/qLd1LNnT8bnYozPvbw8NknqYvNR10g1mvqoP4LWaPf9FLQLNTtxeP264eXxeXlsEuNzu1jVbOr1LQkz8U5PT1d6enqHPd6FCxdUVVWlYDDYYY8JALg7ycnJCgQCOlht8fHhdgoEAqySfReo2QAAO9TrthJm4h2JyspKXbx4UZWVlWpqatKxY8ckSUOGDFGPHj0kSUOHDtXq1auVn5+vf/75RytWrNCsWbMUDAZ15swZLVu2TOnp6crPz4/jSAAAkUhNTVVFRYUaGmxWBWyH5ORkpaamxigq2KFmA0DnQ71uy5UT7/fee0/btm0L/TxixAhJUlFRkSZMmCBJOnnyZGhF065du6q8vFyfffaZLl++rGAwqIkTJ2r79u1KS0tr9+OmpKRo+fLllgu7uB3jczfG515eHpsU+/GlpqZ6pgh3BtRsZzA+9/Ly2CTG53axHB/1ujWf8dq31gEAAAAASCCxW+kGAAAAAAC0wcQbAAAAAAAHMfEGAAAAAMBBTLwBAAAAAHAQE28AAAAAABzExPsOVq1apTFjxqh79+7q1atXu85ZsGCBfD5fq1tOTo6zgUYpmvEZY7RixQr1799f99xzjyZMmKDff//d2UCjdOnSJRUUFMjv98vv96ugoECXL1+2PSeR8/fpp59q8ODBSk1N1ahRo/Tjjz/aHr9//36NGjVKqampeuCBB7Rp06YOijRykYytuLi4TY58Pp9OnDjRgRG334EDB/Tss8+qf//+8vl8+uabb+54jptyF+n43JY/uIeXazb1uq1Ezp2X67Xk3ZpNvW7NTblzAybed9DQ0KDZs2frtddei+i8qVOn6s8//wzdvvvuO4civDvRjO+DDz7Q+vXrtWHDBpWWlioQCOjpp59WXV2dg5FG58UXX9SxY8e0d+9e7d27V8eOHVNBQcEdz0vE/G3fvl2LFy/WO++8o7KyMo0dO1bTpk1TZWVl2OMrKio0ffp0jR07VmVlZVq2bJkWLVqkHTt2dHDkdxbp2G46efJkqzw99NBDHRRxZK5cuaLHHntMGzZsaNfxbsqdFPn4bnJL/uAeXq7Z1OvwEjF3Xq7XkrdrNvU6PDfkzhUM2mXLli3G7/e369jCwkIzY8YMR+OJtfaOr7m52QQCAbNmzZrQtmvXrhm/3282bdrkYISRO378uJFkfvrpp9C2kpISI8mcOHHC8rxEzd/o0aPNq6++2mrb0KFDzdKlS8Me/9Zbb5mhQ4e22vbKK6+YnJwcx2KMVqRjKyoqMpLMpUuXOiC62JJkdu3aZXuMm3J3u/aMz835gzt4uWZTr29J1Nx5uV4b03lqNvXavblLVLzj7ZDi4mJlZGTo4Ycf1ssvv6xz587FO6SYqKioUHV1tSZPnhzalpKSovHjx+vQoUNxjKytkpIS+f1+PfHEE6FtOTk58vv9d4w10fLX0NCgI0eOtHreJWny5MmWYykpKWlz/JQpU/TLL7/o+vXrjsUaqWjGdtOIESMUDAY1adIkFRUVORlmh3JL7u6WV/MH90m0a34sUK/jw8v1WqJm385NubsbXsxdPDDxdsC0adP0xRdf6IcfftCHH36o0tJS5eXlqb6+Pt6h3bXq6mpJUr9+/Vpt79evX2hfoqiurlZGRkab7RkZGbaxJmL+zp8/r6ampoie9+rq6rDHNzY26vz5847FGqloxhYMBvW///1PO3bs0M6dO5WVlaVJkybpwIEDHRGy49ySu2h5PX9wl0S85scC9To+vFyvJWr27dyUu2h4OXfx0C3eAcTDihUrtHLlSttjSktLlZ2dHdX9z5kzJ/Tv4cOHKzs7W5mZmdqzZ49mzpwZ1X1GwunxSZLP52v1szGmzTantHd8Uts4pTvHGu/82Yn0eQ93fLjtiSCSsWVlZSkrKyv0c25urqqqqrRu3TqNGzfO0Tg7iptyF6nOkD/EjpdrNvWaem13fLjtiYKafYvbchcJr+euo3XKiffChQs1d+5c22MGDRoUs8cLBoPKzMzU6dOnY3afdpwcXyAQkHTjFb5gMBjafu7cuTav+DmlveP79ddf9ddff7XZ9/fff0cUa0fnL5z09HR17dq1zavJds97IBAIe3y3bt103333ORZrpKIZWzg5OTn6/PPPYx1eXLgld7Hkpfwhtrxcs6nX1GvJXdd8anZrbspdrHgld/HQKSfe6enpSk9P77DHu3DhgqqqqloVPic5Ob7BgwcrEAho3759GjFihKQb3/fZv3+/1q5d68hj3q6948vNzVVNTY0OHz6s0aNHS5J+/vln1dTUaMyYMe1+vI7OXzjJyckaNWqU9u3bp/z8/ND2ffv2acaMGWHPyc3N1e7du1tt+/7775Wdna2kpCRH441ENGMLp6ysLK45iiW35C6WvJQ/xJaXazb1+gbqtXuu+dTs1tyUu1jxSu7iIj5rurnH2bNnTVlZmVm5cqXp0aOHKSsrM2VlZaauri50TFZWltm5c6cxxpi6ujqzZMkSc+jQIVNRUWGKiopMbm6uuf/++01tbW28hmEp0vEZY8yaNWuM3+83O3fuNOXl5WbevHkmGAwm5PimTp1qHn30UVNSUmJKSkrMI488Yp555plWx7glf1999ZVJSkoymzdvNsePHzeLFy829957rzlz5owxxpilS5eagoKC0PF//PGH6d69u3n99dfN8ePHzebNm01SUpL5+uuv4zUES5GO7aOPPjK7du0yp06dMr/99ptZunSpkWR27NgRryHYqqurC/1uSTLr1683ZWVl5uzZs8YYd+fOmMjH57b8wT28XLOp1+7JnZfrtTHertnUa/fmzg2YeN9BYWGhkdTmVlRUFDpGktmyZYsxxph///3XTJ482fTt29ckJSWZgQMHmsLCQlNZWRmfAdxBpOMz5kaLkuXLl5tAIGBSUlLMuHHjTHl5eccH3w4XLlww8+fPN2lpaSYtLc3Mnz+/TUsEN+Xvk08+MZmZmSY5OdmMHDnS7N+/P7SvsLDQjB8/vtXxxcXFZsSIESY5OdkMGjTIbNy4sYMjbr9IxrZ27Vrz4IMPmtTUVNO7d2/z1FNPmT179sQh6va52Y7j9lthYaExxv25i3R8bssf3MPLNZt67a7cebleG+Pdmk29dm/u3MBnzH8rAAAAAAAAgJijnRgAAAAAAA5i4g0AAAAAgIOYeAMAAAAA4CAm3gAAAAAAOIiJNwAAAAAADmLiDQAAAACAg5h4AwAAAADgICbeAAAAAAA4iIk3AAAAAAAOYuINuNjHH3+swYMHq3v37nr++edVU1MT75AAAMBtqNcAmHgDLrVs2TJt2LBB27Zt08GDB1VWVqaVK1fGOywAANAC9RqAJPmMMSbeQQCITGlpqXJyclRaWqqRI0dKkt5//31t3bpVp06dinN0AABAol4DuIV3vAEXWrdunfLy8kJFXJL69u2r8+fPxzEqAADQEvUawE1MvAGXqa+v1+7du5Wfn99q+9WrV+X3++MUFQAAaIl6DaAlJt6Ayxw9elRXr17VkiVL1KNHj9DtzTffVFZWliQpPz9fvXv31gsvvBDnaAEA6Jyo1wBa6hbvAABE5tSpU0pNTVV5eXmr7c8995yefPJJSdKiRYv00ksvadu2bfEIEQCATo96DaAl3vEGXKa2tlYZGRkaMmRI6JacnKwTJ05o1qxZkqSJEycqLS0tzpECANB5Ua8BtMTEG3CZ9PR01dbWqmVDglWrVmn69OkaNmxYHCMDAAA3Ua8BtMRHzQGXycvL07Vr17RmzRrNmzdPX375pb799lsdPnw43qEBAID/UK8BtMQ73oDL9OvXT1u3btXGjRs1bNgwHTp0SAcPHtSAAQPiHRoAAPgP9RpAS7zjDbjQnDlzNGfOnHiHAQAAbFCvAdzkMy2/eALAE6ZMmaKjR4/qypUr6tOnj3bt2qXHH3883mEBAIAWqNdA58HEGwAAAAAAB/EdbwAAAAAAHMTEGwAAAAAABzHxBgAAAADAQUy8AQAAAABwEBNvAAAAAAAcxMQbAAAAAAAHMfEGAAAAAMBBTLwBAAAAAHAQE28AAAAAABzExBsAAAAAAAcx8QYAAAAAwEH/D4TnUvuxdmYDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1000x1000 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N = 10000000  # number of random samles\n",
    "M = 50  # number of bins for bivariate/marginal histograms\n",
    "\n",
    "\n",
    "def compute_plot_histograms(kappa):\n",
    "    \"\"\"Estimate and plot bivariate/product PDFs for given shift\"\"\"\n",
    "\n",
    "    # shift signal\n",
    "    x2 = np.concatenate((x1[kappa:], np.zeros(kappa)))\n",
    "\n",
    "    # compute bivariate and marginal histograms\n",
    "    pdf_xx, x1edges, x2edges = np.histogram2d(\n",
    "        x1, x2, bins=(M, M), range=((-1.5, 1.5), (-1.5, 1.5)), density=True\n",
    "    )\n",
    "    pdf_x1, _ = np.histogram(x1, bins=M, range=(-1.5, 1.5), density=True)\n",
    "    pdf_x2, _ = np.histogram(x2, bins=M, range=(-1.5, 1.5), density=True)\n",
    "\n",
    "    # plot results\n",
    "    fig = plt.figure(figsize=(10, 10))\n",
    "\n",
    "    plt.subplot(121, aspect=\"equal\")\n",
    "    plt.pcolormesh(x1edges, x2edges, pdf_xx)\n",
    "    plt.xlabel(r\"$\\theta_1$\")\n",
    "    plt.ylabel(r\"$\\theta_2$\")\n",
    "    plt.title(r\"Bivariate PDF $p_{{xy}}(\\theta_1, \\theta_2, \\kappa)$\")\n",
    "    plt.colorbar(fraction=0.046)\n",
    "\n",
    "    plt.subplot(122, aspect=\"equal\")\n",
    "    plt.pcolormesh(x1edges, x2edges, np.outer(pdf_x1, pdf_x2))\n",
    "    plt.xlabel(r\"$\\theta_1$\")\n",
    "    plt.ylabel(r\"$\\theta_2$\")\n",
    "    plt.title(r\"Product of PDFs $p_x(\\theta_1) \\cdot p_x(\\theta_2, \\kappa)$\")\n",
    "    plt.colorbar(fraction=0.046)\n",
    "\n",
    "    fig.suptitle(\"Shift $\\kappa =$ {:<2.0f}\".format(kappa), y=0.72)\n",
    "    fig.tight_layout()\n",
    "\n",
    "\n",
    "# generate signal\n",
    "x = np.random.normal(size=N)\n",
    "x1 = np.convolve(x, [1, 0.5, 0.3, 0.7, 0.3], mode=\"same\")\n",
    "\n",
    "# compute and plot the PDFs for various shifts\n",
    "compute_plot_histograms(0)\n",
    "compute_plot_histograms(2)\n",
    "compute_plot_histograms(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "* With the given results, how can you evaluate the independence of the random signal?\n",
    "* Can the random signal assumed to be independent?\n",
    "\n",
    "Solution: According to the definition of independence, the bivariate PDF and the product of the univariate PDFs has to be equal for $\\kappa \\neq 0$. This is obviously not the case for $\\kappa=2$. Hence, the random signal is not independent in a strict sense. However for $\\kappa=20$ the condition for independence is sufficiently fulfilled, considering the statistical uncertainty due to a finite number of samples. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Independence versus Uncorrelatedness \n",
    "\n",
    "Two continuous-amplitude real-valued jointly WSS random processes $x[k]$ and $y[k]$ are termed as [uncorrelated](correlation_functions.ipynb#Properties) if their cross-correlation function (CCF) is equal to the product of their linear means, $\\varphi_{xy}[\\kappa] = \\mu_x \\cdot \\mu_y$. If two random signals are independent then they are also uncorrelated. This can be proven by introducing above findings for the linear second-order ensemble average of independent random signals into the definition of the CCF\n",
    "\n",
    "\\begin{equation}\n",
    "\\varphi_{xy}[\\kappa] = E \\{ x[k] \\cdot y[k - \\kappa] \\} = E \\{ x[k] \\} \\cdot E \\{ y[k - \\kappa] \\} = \\mu_x \\cdot \\mu_y\n",
    "\\end{equation}\n",
    "\n",
    "where the last equality is a consequence of the assumed wide-sense stationarity. The reverse, that two uncorrelated signals are also independent does not hold in general from this result.\n",
    "\n",
    "The auto-correlation function (ACF) of an [uncorrelated signal](correlation_functions.ipynb#Properties) is given as $\\varphi_{xx}[\\kappa] = \\mu_x^2 + \\sigma_x^2 \\cdot \\delta[\\kappa]$. Introducing the definition of independence into the definition of the ACF yields\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\varphi_{xx}[\\kappa] &= E \\{ x[k] \\cdot x[k - \\kappa] \\} \\\\\n",
    "&= \n",
    "\\begin{cases}\n",
    "E \\{ x^2[k] \\} & \\text{for } \\kappa = 0 \\\\\n",
    "E \\{ x[k] \\} \\cdot E \\{ x[k - \\kappa] \\} & \\text{for } \\kappa \\neq 0\n",
    "\\end{cases} \\\\\n",
    "&= \n",
    "\\begin{cases}\n",
    "\\mu_x^2 + \\sigma_x^2 & \\text{for } \\kappa = 0 \\\\\n",
    "\\mu_x^2 & \\text{for } \\kappa \\neq 0\n",
    "\\end{cases} \\\\\n",
    "&= \\mu_x^2 + \\sigma_x^2 \\delta[\\kappa]\n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "where the result for $\\kappa = 0$ follows from the bivariate PDF $p_{xx}(\\theta_1, \\theta_2, \\kappa)$ of an independent signal, as derived above. It can be concluded from this result that an independent random signal is also uncorrelated. The reverse, that an uncorrelated signal is independent does not hold in general."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Independence versus Orthogonality\n",
    "\n",
    "In geometry, two vectors are said to be [orthogonal](https://en.wikipedia.org/wiki/Orthogonality) if their dot product equals zero. This definition is frequently applied to finite-length random signals by interpreting them as vectors. The relation between independence, correlatedness and orthogonality is derived in the following.\n",
    "\n",
    "Let's assume two continuous-amplitude real-valued jointly wide-sense ergodic random signals $x_N[k]$ and $y_M[k]$ with finite lengths $N$ and $M$, respectively. The CCF $\\varphi_{xy}[\\kappa]$ between both can be reformulated as follows\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "\\varphi_{xy}[\\kappa] &= \\frac{1}{N} \\sum_{k=0}^{N-1} x_N[k] \\cdot y_M[k-\\kappa] \\\\\n",
    "&= \\frac{1}{N} < \\mathbf{x}_N, \\mathbf{y}_M[\\kappa] > \n",
    "\\end{split}\n",
    "\\end{equation}\n",
    "\n",
    "where $<\\cdot, \\cdot>$ denotes the [dot product](https://en.wikipedia.org/wiki/Dot_product). The $(N+2M-2) \\times 1$ vector $\\mathbf{x}_N$ is defined as \n",
    "\n",
    "$$\\mathbf{x}_N = \\left[ \\mathbf{0}^T_{(M-1) \\times 1}, x[0], x[1], \\dots, x[N-1], \\mathbf{0}^T_{(M-1) \\times 1} \\right]^T$$\n",
    "\n",
    "where $\\mathbf{0}_{(M-1) \\times 1}$ denotes the zero vector of length $M-1$. The $(N+2M-2) \\times 1$ vector $\\mathbf{y}_M[\\kappa]$ is defined as \n",
    "\n",
    "$$\\mathbf{y}_M = \\left[ \\mathbf{0}^T_{\\kappa \\times 1}, y[0], y[1], \\dots, y[M-1], \\mathbf{0}^T_{(N+M-2-\\kappa) \\times 1}  \\right]^T$$\n",
    "\n",
    "It follows from above definition of orthogonality that two finite-length random signals are orthogonal if their CCF is zero. This implies that at least one of the two signals has to be mean free. It can be concluded further that two independent random signals are also orthogonal and uncorrelated if at least one of them is mean free. The reverse, that orthogonal signals are independent, does not hold in general.\n",
    "\n",
    "The concept of orthogonality can also be extended to one random signal by setting $\\mathbf{y}_M[\\kappa] = \\mathbf{x}_N[\\kappa]$. Since a random signal cannot be orthogonal to itself for $\\kappa = 0$, the definition of orthogonality has to be extended for this case. According to the ACF of a mean-free uncorrelated random signal $x[k]$, self-orthogonality may be defined as\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{1}{N} < \\mathbf{x}_N, \\mathbf{x}_N[\\kappa] > =\n",
    "\\begin{cases}\n",
    "\\sigma_x^2 & \\text{for } \\kappa = 0 \\\\\n",
    "0 & \\text{for } \\kappa \\neq 0\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "\n",
    "An independent random signal is also orthogonal if it is zero-mean. The reverse, that an orthogonal signal is independent does not hold in general."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example - Computation of cross-correlation by dot product\n",
    "\n",
    "This example illustrates the computation of the CCF by the dot product. First, a function is defined which computes the CCF by means of the dot product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ccf_by_dotprod(x, y):\n",
    "    \"\"\"Computes the CCF by the dot product.\"\"\"\n",
    "\n",
    "    N = len(x)\n",
    "    M = len(y)\n",
    "    xN = np.concatenate((np.zeros(M - 1), x, np.zeros(M - 1)))\n",
    "    yM = np.concatenate((y, np.zeros(N + M - 2)))\n",
    "\n",
    "    return np.fromiter(\n",
    "        [np.dot(xN, np.roll(yM, kappa)) for kappa in range(N + M - 1)], float\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the CCF is computed using different methods: computation by the dot product and by the built-in correlation function. The CCF is plotted for the computation by the dot product, as well as the difference (magnitude) between both methods. The resulting difference is in the typical expected range due to numerical inaccuracies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 32  # length of signals\n",
    "\n",
    "# generate signals\n",
    "np.random.seed(1)\n",
    "x = np.random.normal(size=N)\n",
    "y = np.convolve(x, [1, 0.5, 0.3, 0.7, 0.3], mode=\"same\")\n",
    "\n",
    "# compute CCF\n",
    "ccf1 = 1 / N * np.correlate(x, y, mode=\"full\")\n",
    "ccf2 = 1 / N * ccf_by_dotprod(x, y)\n",
    "kappa = np.arange(-N + 1, N)\n",
    "\n",
    "# plot results\n",
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.stem(kappa, ccf1)\n",
    "plt.xlabel(\"$\\kappa$\")\n",
    "plt.ylabel(r\"$\\varphi_{xy}[\\kappa]$\")\n",
    "plt.title(\"CCF by dot product\")\n",
    "plt.grid()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.stem(kappa, np.abs(ccf1 - ccf2))\n",
    "plt.xlabel(\"$\\kappa$\")\n",
    "plt.title(\"Difference (magnitude)\")\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
